LMFDB - Embedded newform 231.2.u.a.20.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(20,231)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 6]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("231.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.u (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			20.18
Character	$\chi$	$=$	231.20
Dual form			231.2.u.a.104.18

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.606621 + 0.197103i) q^{2} +(1.57241 - 0.726320i) q^{3} +(-1.28889 - 0.936436i) q^{4} +(-0.284064 - 0.874260i) q^{5} +(1.09702 - 0.130675i) q^{6} +(-0.678241 - 2.55734i) q^{7} +(-1.34712 - 1.85415i) q^{8} +(1.94492 - 2.28414i) q^{9} +O(q^{10})$	\(q+(0.606621 + 0.197103i) q^{2} +(1.57241 - 0.726320i) q^{3} +(-1.28889 - 0.936436i) q^{4} +(-0.284064 - 0.874260i) q^{5} +(1.09702 - 0.130675i) q^{6} +(-0.678241 - 2.55734i) q^{7} +(-1.34712 - 1.85415i) q^{8} +(1.94492 - 2.28414i) q^{9} -0.586335i q^{10} +(-2.52823 + 2.14664i) q^{11} +(-2.70682 - 0.536309i) q^{12} +(6.23392 + 2.02552i) q^{13} +(0.0926247 - 1.68502i) q^{14} +(-1.08166 - 1.16837i) q^{15} +(0.532894 + 1.64008i) q^{16} +(1.08749 + 3.34694i) q^{17} +(1.63004 - 1.00226i) q^{18} +(-0.0854645 - 0.117632i) q^{19} +(-0.452560 + 1.39284i) q^{20} +(-2.92392 - 3.52856i) q^{21} +(-1.95679 + 0.803875i) q^{22} +5.77943i q^{23} +(-3.46493 - 1.93704i) q^{24} +(3.36145 - 2.44223i) q^{25} +(3.38239 + 2.45745i) q^{26} +(1.39919 - 5.00423i) q^{27} +(-1.52061 + 3.93127i) q^{28} +(-0.170143 + 0.234182i) q^{29} +(-0.425867 - 0.921956i) q^{30} +(-3.91775 - 1.27295i) q^{31} +5.68366i q^{32} +(-2.41626 + 5.21169i) q^{33} +2.24467i q^{34} +(-2.04312 + 1.31941i) q^{35} +(-4.64575 + 1.12272i) q^{36} +(-1.56403 - 1.13634i) q^{37} +(-0.0286590 - 0.0882033i) q^{38} +(11.2734 - 1.34287i) q^{39} +(-1.23834 + 1.70443i) q^{40} +(6.50747 - 4.72795i) q^{41} +(-1.07822 - 2.71681i) q^{42} +3.78771 q^{43} +(5.26881 - 0.399264i) q^{44} +(-2.54941 - 1.05152i) q^{45} +(-1.13914 + 3.50593i) q^{46} +(-2.58114 + 1.87530i) q^{47} +(2.02915 + 2.19182i) q^{48} +(-6.07998 + 3.46899i) q^{49} +(2.52050 - 0.818960i) q^{50} +(4.14092 + 4.47289i) q^{51} +(-6.13808 - 8.44835i) q^{52} +(-10.7279 - 3.48570i) q^{53} +(1.83513 - 2.75989i) q^{54} +(2.59490 + 1.60055i) q^{55} +(-3.82803 + 4.70261i) q^{56} +(-0.219823 - 0.122890i) q^{57} +(-0.149371 + 0.108524i) q^{58} +(4.30990 + 3.13133i) q^{59} +(0.300037 + 2.51881i) q^{60} +(3.18676 - 1.03544i) q^{61} +(-2.12569 - 1.54440i) q^{62} +(-7.16044 - 3.42463i) q^{63} +(-0.0544799 + 0.167672i) q^{64} -6.02544i q^{65} +(-2.49299 + 2.68527i) q^{66} -5.90336 q^{67} +(1.73254 - 5.33222i) q^{68} +(4.19771 + 9.08761i) q^{69} +(-1.49946 + 0.397676i) q^{70} +(-5.71118 + 1.85568i) q^{71} +(-6.85519 - 0.529168i) q^{72} +(-4.90051 + 6.74497i) q^{73} +(-0.724801 - 0.997603i) q^{74} +(3.51172 - 6.28167i) q^{75} +0.231647i q^{76} +(7.20443 + 5.00960i) q^{77} +(7.10338 + 1.40741i) q^{78} +(-1.96364 + 6.04346i) q^{79} +(1.28248 - 0.931776i) q^{80} +(-1.43457 - 8.88493i) q^{81} +(4.87947 - 1.58544i) q^{82} +(4.62359 + 14.2299i) q^{83} +(0.464349 + 7.28600i) q^{84} +(2.61718 - 1.90149i) q^{85} +(2.29771 + 0.746570i) q^{86} +(-0.0974433 + 0.491808i) q^{87} +(7.38603 + 1.79594i) q^{88} -14.2572 q^{89} +(-1.33927 - 1.14037i) q^{90} +(0.951853 - 17.3160i) q^{91} +(5.41207 - 7.44907i) q^{92} +(-7.08487 + 0.843939i) q^{93} +(-1.93540 + 0.628850i) q^{94} +(-0.0785634 + 0.108133i) q^{95} +(4.12816 + 8.93702i) q^{96} +(13.3252 + 4.32964i) q^{97} +(-4.37199 + 0.905977i) q^{98} +(-0.0139835 + 9.94986i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9}+O(q^{10}) $ 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9	$ 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9} - 60 q^{16} + 2 q^{18} - 80 q^{22} - 36 q^{25} + 8 q^{28} + 24 q^{30} - 34 q^{36} + 4 q^{37} - 66 q^{39} - 30 q^{42} + 36 q^{46} + 26 q^{49} + 38 q^{51} - 86 q^{57} - 116 q^{58} + 88 q^{60} + 44 q^{63} - 32 q^{64} + 110 q^{70} + 86 q^{72} - 52 q^{78} - 156 q^{79} + 68 q^{81} - 30 q^{84} + 8 q^{85} - 112 q^{88} + 42 q^{91} + 56 q^{93} + 70 q^{99}+O(q^{100}) $ 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9 - 60 * q^16 + 2 * q^18 - 80 * q^22 - 36 * q^25 + 8 * q^28 + 24 * q^30 - 34 * q^36 + 4 * q^37 - 66 * q^39 - 30 * q^42 + 36 * q^46 + 26 * q^49 + 38 * q^51 - 86 * q^57 - 116 * q^58 + 88 * q^60 + 44 * q^63 - 32 * q^64 + 110 * q^70 + 86 * q^72 - 52 * q^78 - 156 * q^79 + 68 * q^81 - 30 * q^84 + 8 * q^85 - 112 * q^88 + 42 * q^91 + 56 * q^93 + 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.606621	+	0.197103i	0.428946	+	0.139373i	0.515530	−	0.856872i	$-0.327595\pi$
$2$	0.606621	+	0.197103i	0.428946	+	0.139373i	−0.0865839	+	0.996245i	$0.527595\pi$
$3$	1.57241	−	0.726320i	0.907829	−	0.419341i
$3$	1.57241	−	0.726320i	0.907829	−	0.419341i
$4$	−1.28889	−	0.936436i	−0.644447	−	0.468218i
$5$	−0.284064	−	0.874260i	−0.127037	−	0.390981i	0.867229	−	0.497909i	$-0.165899\pi$
$5$	−0.284064	−	0.874260i	−0.127037	−	0.390981i	−0.994267	+	0.106928i	$0.965899\pi$
$6$	1.09702	−	0.130675i	0.447855	−	0.0533477i
$7$	−0.678241	−	2.55734i	−0.256351	−	0.966584i
$7$	−0.678241	−	2.55734i	−0.256351	−	0.966584i
$8$	−1.34712	−	1.85415i	−0.476279	−	0.655542i
$9$	1.94492	−	2.28414i	0.648307	−	0.761379i
$10$		−	0.586335i		−	0.185415i
$11$	−2.52823	+	2.14664i	−0.762290	+	0.647236i
$11$	−2.52823	+	2.14664i	−0.762290	+	0.647236i
$12$	−2.70682	−	0.536309i	−0.781391	−	0.154819i
$13$	6.23392	+	2.02552i	1.72898	+	0.561779i	0.993301	−	0.115555i	$-0.0368647\pi$
$13$	6.23392	+	2.02552i	1.72898	+	0.561779i	0.735676	+	0.677334i	$0.236865\pi$
$14$	0.0926247	−	1.68502i	0.0247550	−	0.450341i
$15$	−1.08166	−	1.16837i	−0.279283	−	0.301672i
$16$	0.532894	+	1.64008i	0.133224	+	0.410020i
$17$	1.08749	+	3.34694i	0.263754	+	0.811753i	0.991978	+	0.126413i	$0.0403464\pi$
$17$	1.08749	+	3.34694i	0.263754	+	0.811753i	−0.728223	+	0.685340i	$0.759654\pi$
$18$	1.63004	−	1.00226i	0.384204	−	0.236234i
$19$	−0.0854645	−	0.117632i	−0.0196069	−	0.0269866i	0.799101	−	0.601197i	$-0.205309\pi$
$19$	−0.0854645	−	0.117632i	−0.0196069	−	0.0269866i	−0.818708	+	0.574210i	$0.805309\pi$
$20$	−0.452560	+	1.39284i	−0.101196	+	0.311448i
$21$	−2.92392	−	3.52856i	−0.638051	−	0.769994i
$22$	−1.95679	+	0.803875i	−0.417189	+	0.171387i
$23$			5.77943i			1.20509i	0.798083	+	0.602547i	$0.205848\pi$
$23$			5.77943i			1.20509i	−0.798083	+	0.602547i	$0.794152\pi$
$24$	−3.46493	−	1.93704i	−0.707276	−	0.395397i
$25$	3.36145	−	2.44223i	0.672289	−	0.488447i
$26$	3.38239	+	2.45745i	0.663341	+	0.481946i
$27$	1.39919	−	5.00423i	0.269274	−	0.963064i
$28$	−1.52061	+	3.93127i	−0.287367	+	0.742940i
$29$	−0.170143	+	0.234182i	−0.0315948	+	0.0434866i	−0.824522	−	0.565830i	$-0.808556\pi$
$29$	−0.170143	+	0.234182i	−0.0315948	+	0.0434866i	0.792927	+	0.609316i	$0.208556\pi$
$30$	−0.425867	−	0.921956i	−0.0777522	−	0.168325i
$31$	−3.91775	−	1.27295i	−0.703649	−	0.228629i	−0.0647293	−	0.997903i	$-0.520618\pi$
$31$	−3.91775	−	1.27295i	−0.703649	−	0.228629i	−0.638920	+	0.769273i	$0.720618\pi$
$32$			5.68366i			1.00474i
$33$	−2.41626	+	5.21169i	−0.420616	+	0.907239i
$34$			2.24467i			0.384958i
$35$	−2.04312	+	1.31941i	−0.345350	+	0.223021i
$36$	−4.64575	+	1.12272i	−0.774291	+	0.187120i
$37$	−1.56403	−	1.13634i	−0.257126	−	0.186813i	0.451753	−	0.892143i	$-0.350799\pi$
$37$	−1.56403	−	1.13634i	−0.257126	−	0.186813i	−0.708879	+	0.705330i	$0.750799\pi$
$38$	−0.0286590	−	0.0882033i	−0.00464910	−	0.0143085i
$39$	11.2734	−	1.34287i	1.80519	−	0.215032i
$40$	−1.23834	+	1.70443i	−0.195799	+	0.269495i
$41$	6.50747	−	4.72795i	1.01630	−	0.738382i	0.0507759	−	0.998710i	$-0.483831\pi$
$41$	6.50747	−	4.72795i	1.01630	−	0.738382i	0.965520	+	0.260328i	$0.0838306\pi$
$42$	−1.07822	−	2.71681i	−0.166373	−	0.419213i
$43$	3.78771			0.577620			0.288810	−	0.957386i	$-0.406740\pi$
$43$	3.78771			0.577620			0.288810	+	0.957386i	$0.406740\pi$
$44$	5.26881	−	0.399264i	0.794303	−	0.0601913i
$45$	−2.54941	−	1.05152i	−0.380044	−	0.156752i
$46$	−1.13914	+	3.50593i	−0.167958	+	0.516921i
$47$	−2.58114	+	1.87530i	−0.376497	+	0.273541i	−0.759900	−	0.650040i	$-0.774752\pi$
$47$	−2.58114	+	1.87530i	−0.376497	+	0.273541i	0.383403	+	0.923581i	$0.374752\pi$
$48$	2.02915	+	2.19182i	0.292882	+	0.316362i
$49$	−6.07998	+	3.46899i	−0.868568	+	0.495569i
$50$	2.52050	−	0.818960i	0.356452	−	0.115818i
$51$	4.14092	+	4.47289i	0.579845	+	0.626329i
$52$	−6.13808	−	8.44835i	−0.851199	−	1.17158i
$53$	−10.7279	−	3.48570i	−1.47359	−	0.478797i	−0.541396	−	0.840768i	$-0.682104\pi$
$53$	−10.7279	−	3.48570i	−1.47359	−	0.478797i	−0.932190	+	0.361970i	$0.882104\pi$
$54$	1.83513	−	2.75989i	0.249729	−	0.375573i
$55$	2.59490	+	1.60055i	0.349896	+	0.215818i
$56$	−3.82803	+	4.70261i	−0.511542	+	0.628413i
$57$	−0.219823	−	0.122890i	−0.0291163	−	0.0162772i
$58$	−0.149371	+	0.108524i	−0.0196133	+	0.0142499i
$59$	4.30990	+	3.13133i	0.561101	+	0.407664i	0.831862	−	0.554983i	$-0.187275\pi$
$59$	4.30990	+	3.13133i	0.561101	+	0.407664i	−0.270761	+	0.962647i	$0.587275\pi$
$60$	0.300037	+	2.51881i	0.0387345	+	0.325177i
$61$	3.18676	−	1.03544i	0.408023	−	0.132575i	−0.0978119	−	0.995205i	$-0.531184\pi$
$61$	3.18676	−	1.03544i	0.408023	−	0.132575i	0.505835	+	0.862630i	$0.331184\pi$
$62$	−2.12569	−	1.54440i	−0.269963	−	0.196139i
$63$	−7.16044	−	3.42463i	−0.902131	−	0.431462i
$64$	−0.0544799	+	0.167672i	−0.00680999	+	0.0209590i
$65$		−	6.02544i		−	0.747364i
$66$	−2.49299	+	2.68527i	−0.306866	+	0.330534i
$67$	−5.90336			−0.721210			−0.360605	−	0.932719i	$-0.617430\pi$
$67$	−5.90336			−0.721210			−0.360605	+	0.932719i	$0.617430\pi$
$68$	1.73254	−	5.33222i	0.210102	−	0.646626i
$69$	4.19771	+	9.08761i	0.505345	+	1.09402i
$70$	−1.49946	+	0.397676i	−0.179220	+	0.0475314i
$71$	−5.71118	+	1.85568i	−0.677793	+	0.220228i	−0.627629	−	0.778513i	$-0.715974\pi$
$71$	−5.71118	+	1.85568i	−0.677793	+	0.220228i	−0.0501640	+	0.998741i	$0.515974\pi$
$72$	−6.85519	−	0.529168i	−0.807891	−	0.0623631i
$73$	−4.90051	+	6.74497i	−0.573561	+	0.789440i	−0.992971	−	0.118358i	$-0.962237\pi$
$73$	−4.90051	+	6.74497i	−0.573561	+	0.789440i	0.419410	+	0.907797i	$0.362237\pi$
$74$	−0.724801	−	0.997603i	−0.0842564	−	0.115969i
$75$	3.51172	−	6.28167i	0.405498	−	0.725345i
$76$			0.231647i			0.0265717i
$77$	7.20443	+	5.00960i	0.821021	+	0.570897i
$78$	7.10338	+	1.40741i	0.804300	+	0.159358i
$79$	−1.96364	+	6.04346i	−0.220927	+	0.679942i	0.777753	+	0.628570i	$0.216359\pi$
$79$	−1.96364	+	6.04346i	−0.220927	+	0.679942i	−0.998680	+	0.0513722i	$0.983641\pi$
$80$	1.28248	−	0.931776i	0.143386	−	0.104176i
$81$	−1.43457	−	8.88493i	−0.159397	−	0.987215i
$82$	4.87947	−	1.58544i	0.538847	−	0.175082i
$83$	4.62359	+	14.2299i	0.507505	+	1.56194i	0.796519	+	0.604614i	$0.206673\pi$
$83$	4.62359	+	14.2299i	0.507505	+	1.56194i	−0.289014	+	0.957325i	$0.593327\pi$
$84$	0.464349	+	7.28600i	0.0506646	+	0.794968i
$85$	2.61718	−	1.90149i	0.283873	−	0.206246i
$86$	2.29771	+	0.746570i	0.247768	+	0.0805047i
$87$	−0.0974433	+	0.491808i	−0.0104470	+	0.0527274i
$88$	7.38603	+	1.79594i	0.787353	+	0.191448i
$89$	−14.2572			−1.51126			−0.755631	−	0.654997i	$-0.772670\pi$
$89$	−14.2572			−1.51126			−0.755631	+	0.654997i	$0.772670\pi$
$90$	−1.33927	−	1.14037i	−0.141171	−	0.120206i
$91$	0.951853	−	17.3160i	0.0997813	−	1.81521i
$92$	5.41207	−	7.44907i	0.564247	−	0.776620i
$93$	−7.08487	+	0.843939i	−0.734667	+	0.0875123i
$94$	−1.93540	+	0.628850i	−0.199621	+	0.0648609i
$95$	−0.0785634	+	0.108133i	−0.00806043	+	0.0110942i
$96$	4.12816	+	8.93702i	0.421328	+	0.912131i
$97$	13.3252	+	4.32964i	1.35297	+	0.439608i	0.893691	−	0.448682i	$-0.148106\pi$
$97$	13.3252	+	4.32964i	1.35297	+	0.439608i	0.459283	+	0.888290i	$0.348106\pi$
$98$	−4.37199	+	0.905977i	−0.441638	+	0.0915175i
$99$	−0.0139835	+	9.94986i	−0.00140539	+	0.999999i
$100$	−6.61955			−0.661955
$101$	3.97238	−	12.2257i	0.395267	−	1.21651i	−0.533487	−	0.845808i	$-0.679119\pi$
$101$	3.97238	−	12.2257i	0.395267	−	1.21651i	0.928754	−	0.370697i	$-0.120881\pi$
$102$	1.63035	+	3.52954i	0.161429	+	0.349476i
$103$	3.57933	−	4.92652i	0.352682	−	0.485425i	−0.595410	−	0.803422i	$-0.703010\pi$
$103$	3.57933	−	4.92652i	0.352682	−	0.485425i	0.948092	+	0.317997i	$0.103010\pi$
$104$	−4.64221	−	14.2873i	−0.455206	−	1.40098i
$105$	−2.25430	+	3.55860i	−0.219997	+	0.347284i
$106$	−5.82071	−	4.22900i	−0.565358	−	0.410756i
$107$	−5.65793	−	7.78747i	−0.546972	−	0.752843i	0.442625	−	0.896707i	$-0.354047\pi$
$107$	−5.65793	−	7.78747i	−0.546972	−	0.752843i	−0.989597	+	0.143864i	$0.954047\pi$
$108$	−6.48954	+	5.13967i	−0.624457	+	0.494565i
$109$	1.22419			0.117256			0.0586281	−	0.998280i	$-0.481327\pi$
$109$	1.22419			0.117256			0.0586281	+	0.998280i	$0.481327\pi$
$110$	1.25865	+	1.48239i	0.120007	+	0.141340i
$111$	−3.28464	−	0.650795i	−0.311764	−	0.0617707i
$112$	3.83281	−	2.47516i	0.362167	−	0.233881i
$113$	6.69613	+	9.21643i	0.629919	+	0.867009i	0.998028	−	0.0627736i	$-0.0199946\pi$
$113$	6.69613	+	9.21643i	0.629919	+	0.867009i	−0.368109	+	0.929783i	$0.619995\pi$
$114$	−0.109127	−	0.117876i	−0.0102207	−	0.0110401i
$115$	5.05273	−	1.64173i	0.471169	−	0.153092i
$116$	0.438594	−	0.142508i	0.0407224	−	0.0132315i
$117$	16.7510	−	10.2996i	1.54863	−	0.952203i
$118$	1.99728	+	2.74902i	0.183865	+	0.253068i
$119$	7.82169	−	5.05111i	0.717013	−	0.463034i
$120$	−0.709215	+	3.57949i	−0.0647422	+	0.326762i
$121$	1.78389	−	10.8544i	0.162171	−	0.986763i
$122$	2.13725			0.193497
$123$	6.79838	−	12.1608i	0.612989	−	1.09650i
$124$	3.85753	+	5.30943i	0.346416	+	0.476801i
$125$	−6.80846	−	4.94664i	−0.608968	−	0.442441i
$126$	−3.66867	−	3.48880i	−0.326831	−	0.310807i
$127$	−4.77111	−	14.6840i	−0.423368	−	1.30299i	−0.904549	−	0.426370i	$-0.859792\pi$
$127$	−4.77111	−	14.6840i	−0.423368	−	1.30299i	0.481181	−	0.876621i	$-0.340208\pi$
$128$	6.61545	−	9.10539i	0.584729	−	0.804810i
$129$	5.95582	−	2.75109i	0.524380	−	0.242220i
$130$	1.18763	−	3.65516i	0.104162	−	0.320579i
$131$	9.08829			0.794047			0.397024	−	0.917808i	$-0.370043\pi$
$131$	9.08829			0.794047			0.397024	+	0.917808i	$0.370043\pi$
$132$	7.99471	−	4.45465i	0.695851	−	0.387727i
$133$	−0.242859	+	0.298345i	−0.0210586	+	0.0258698i
$134$	−3.58110	−	1.16357i	−0.309360	−	0.100517i
$135$	−4.77245	+	0.198267i	−0.410747	+	0.0170641i
$136$	4.74077	−	6.52511i	0.406517	−	0.559523i
$137$	−9.51199	+	3.09063i	−0.812664	+	0.264051i	−0.685726	−	0.727860i	$-0.740515\pi$
$137$	−9.51199	+	3.09063i	−0.812664	+	0.264051i	−0.126938	+	0.991911i	$0.540515\pi$
$138$	0.755226	+	6.34012i	0.0642891	+	0.539707i
$139$	−1.43974	+	1.98163i	−0.122117	+	0.168080i	−0.865699	−	0.500565i	$-0.833126\pi$
$139$	−1.43974	+	1.98163i	−0.122117	+	0.168080i	0.743582	+	0.668645i	$0.233126\pi$
$140$	3.86890	+	0.212671i	0.326982	+	0.0179740i
$141$	−2.69652	+	4.82347i	−0.227088	+	0.406209i
$142$	−3.83029			−0.321430
$143$	−20.1088	+	8.26098i	−1.68158	+	0.690818i
$144$	4.78261	+	1.97262i	0.398551	+	0.164385i
$145$	0.253068	+	0.0822268i	0.0210162	+	0.00682856i
$146$	−4.30221	+	3.12574i	−0.356054	+	0.258688i
$147$	−7.04060	+	9.87066i	−0.580699	+	0.814118i
$148$	0.951767	+	2.92924i	0.0782348	+	0.240782i
$149$	10.0597	−	3.26860i	0.824123	−	0.267774i	0.133555	−	0.991041i	$-0.457361\pi$
$149$	10.0597	−	3.26860i	0.824123	−	0.267774i	0.690568	+	0.723268i	$0.257361\pi$
$150$	3.36842	−	3.11842i	0.275030	−	0.254618i
$151$	−12.4694	+	9.05956i	−1.01475	+	0.737256i	−0.965199	−	0.261515i	$-0.915778\pi$
$151$	−12.4694	+	9.05956i	−1.01475	+	0.737256i	−0.0495470	+	0.998772i	$0.515778\pi$
$152$	−0.102976	+	0.316929i	−0.00835249	+	0.0257063i
$153$	9.75995	+	4.02556i	0.789045	+	0.325447i
$154$	3.38295	+	4.45895i	0.272606	+	0.359313i
$155$			3.78673i			0.304158i
$156$	−15.7878	−	8.82602i	−1.26403	−	0.706647i
$157$	0.909416	+	1.25170i	0.0725793	+	0.0998968i	0.843763	−	0.536716i	$-0.180335\pi$
$157$	0.909416	+	1.25170i	0.0725793	+	0.0998968i	−0.771184	+	0.636612i	$0.780335\pi$
$158$	−2.38237	+	3.27905i	−0.189531	+	0.260867i
$159$	−19.4003	+	2.31093i	−1.53854	+	0.183269i
$160$	4.96900	−	1.61453i	0.392834	−	0.127639i
$161$	14.7800	−	3.91985i	1.16483	−	0.308927i
$162$	0.881005	−	5.67255i	0.0692183	−	0.445678i
$163$	−5.12784	+	15.7819i	−0.401644	+	1.23613i	0.522022	+	0.852932i	$0.325178\pi$
$163$	−5.12784	+	15.7819i	−0.401644	+	1.23613i	−0.923665	+	0.383200i	$0.874822\pi$
$164$	−12.8149			−1.00067
$165$	5.24274	+	0.631982i	0.408147	+	0.0491997i
$166$			9.54351i			0.740720i
$167$	0.535930	−	1.64942i	0.0414715	−	0.127636i	−0.928177	−	0.372139i	$-0.878625\pi$
$167$	0.535930	−	1.64942i	0.0414715	−	0.127636i	0.969649	+	0.244502i	$0.0786246\pi$
$168$	−2.60362	+	10.1748i	−0.200873	+	0.785002i
$169$	24.2417	+	17.6127i	1.86475	+	1.35482i
$170$	1.96243	−	0.637632i	0.150511	−	0.0489041i
$171$	−0.434909	−	0.0335717i	−0.0332583	−	0.00256729i
$172$	−4.88196	−	3.54695i	−0.372246	−	0.270452i
$173$	9.18868	−	6.67596i	0.698602	−	0.507564i	−0.180875	−	0.983506i	$-0.557893\pi$
$173$	9.18868	−	6.67596i	0.698602	−	0.507564i	0.879477	+	0.475942i	$0.157893\pi$
$174$	−0.156048	+	0.279135i	−0.0118300	+	0.0211612i
$175$	−8.52549	−	6.93994i	−0.644467	−	0.524610i
$176$	−4.86794	−	3.00257i	−0.366935	−	0.226327i
$177$	9.05125	+	1.79335i	0.680334	+	0.134796i
$178$	−8.64873	−	2.81014i	−0.648250	−	0.210629i
$179$	−10.4264	−	14.3508i	−0.779309	−	1.07263i	−0.995358	−	0.0962447i	$-0.969317\pi$
$179$	−10.4264	−	14.3508i	−0.779309	−	1.07263i	0.216048	−	0.976383i	$-0.430683\pi$
$180$	2.30124	+	3.74267i	0.171524	+	0.278962i
$181$	−8.98074	+	2.91802i	−0.667533	+	0.216895i	−0.623129	−	0.782119i	$-0.714139\pi$
$181$	−8.98074	+	2.91802i	−0.667533	+	0.216895i	−0.0444041	+	0.999014i	$0.514139\pi$
$182$	3.99046	−	10.3167i	0.295793	−	0.764722i
$183$	4.25882	−	3.94275i	0.314821	−	0.291456i
$184$	10.7160	−	7.78560i	0.789991	−	0.573962i
$185$	−0.549168	+	1.69017i	−0.0403756	+	0.124263i
$186$	−4.46418	−	0.884499i	−0.327329	−	0.0648546i
$187$	−9.93409	−	6.12739i	−0.726453	−	0.448079i
$188$	5.08291			0.370710
$189$	−13.7465	−	0.184131i	−0.999910	−	0.0133936i
$190$	−0.0689716	+	0.0501108i	−0.00500373	+	0.00363542i
$191$	0.957730	−	1.31820i	0.0692989	−	0.0953817i	−0.772961	−	0.634454i	$-0.781225\pi$
$191$	0.957730	−	1.31820i	0.0692989	−	0.0953817i	0.842260	+	0.539072i	$0.181225\pi$
$192$	0.0361189	+	0.303218i	0.00260665	+	0.0218829i
$193$	3.40317	+	10.4739i	0.244965	+	0.753926i	0.995642	+	0.0932562i	$0.0297276\pi$
$193$	3.40317	+	10.4739i	0.244965	+	0.753926i	−0.750677	+	0.660670i	$0.770272\pi$
$194$	7.23000	+	5.25290i	0.519084	+	0.377136i
$195$	−4.37640	−	9.47444i	−0.313400	−	0.678479i
$196$	11.0849	+	1.22236i	0.791781	+	0.0873113i
$197$			0.607768i			0.0433017i	0.999766	+	0.0216508i	$0.00689221\pi$
$197$			0.607768i			0.0433017i	−0.999766	+	0.0216508i	$0.993108\pi$
$198$	−1.96963	+	6.03305i	−0.139976	+	0.428750i
$199$			6.00328i			0.425561i	0.977100	+	0.212781i	$0.0682519\pi$
$199$			6.00328i			0.425561i	−0.977100	+	0.212781i	$0.931748\pi$
$200$	−9.05655	−	2.94265i	−0.640395	−	0.208077i
$201$	−9.28248	+	4.28773i	−0.654735	+	0.302433i
$202$	4.81946	−	6.63342i	0.339096	−	0.466726i
$203$	0.714282	+	0.276283i	0.0501328	+	0.0193912i
$204$	−1.14863	−	9.64279i	−0.0804205	−	0.675130i
$205$	−5.98200	−	4.34618i	−0.417801	−	0.303550i
$206$	3.14233	−	2.28304i	0.218937	−	0.159067i
$207$	13.2010	+	11.2405i	0.917534	+	0.781271i
$208$			11.3035i			0.783757i
$209$	0.468587	+	0.113939i	0.0324128	+	0.00788131i
$210$	−2.06892	+	1.71439i	−0.142769	+	0.118304i
$211$	−5.35273	+	16.4740i	−0.368497	+	1.13412i	0.579265	+	0.815139i	$0.303340\pi$
$211$	−5.35273	+	16.4740i	−0.368497	+	1.13412i	−0.947762	+	0.318978i	$0.896660\pi$
$212$	10.5630	+	14.5387i	0.725467	+	0.998519i
$213$	−7.63248	+	7.06602i	−0.522969	+	0.484156i
$214$	−1.89728	−	5.83924i	−0.129696	−	0.399162i
$215$	−1.07595	−	3.31144i	−0.0733794	−	0.225839i
$216$	−11.1635	+	4.14699i	−0.759579	+	0.282167i
$217$	−0.598199	+	10.8824i	−0.0406084	+	0.738745i
$218$	0.742620	+	0.241292i	0.0502966	+	0.0163424i
$219$	−2.80658	+	14.1652i	−0.189651	+	0.957194i
$220$	−1.84574	−	4.49289i	−0.124440	−	0.302911i
$221$			23.0673i			1.55167i
$222$	−1.86426	−	1.04220i	−0.125121	−	0.0699479i
$223$	−12.6355	−	17.3913i	−0.846137	−	1.16461i	−0.984701	−	0.174254i	$-0.944248\pi$
$223$	−12.6355	−	17.3913i	−0.846137	−	1.16461i	0.138563	−	0.990354i	$-0.455752\pi$
$224$	14.5351	−	3.85489i	0.971165	−	0.257566i
$225$	0.959344	−	12.4280i	0.0639563	−	0.828531i
$226$	2.24543	+	6.91072i	0.149364	+	0.459694i
$227$	−13.1328	−	9.54156i	−0.871657	−	0.633296i	0.0593744	−	0.998236i	$-0.481089\pi$
$227$	−13.1328	−	9.54156i	−0.871657	−	0.633296i	−0.931031	+	0.364940i	$0.881089\pi$
$228$	0.168250	+	0.364243i	0.0111426	+	0.0241226i
$229$	−24.3526	−	7.91264i	−1.60926	−	0.522882i	−0.639890	−	0.768467i	$-0.721020\pi$
$229$	−24.3526	−	7.91264i	−1.60926	−	0.522882i	−0.969375	+	0.245585i	$0.921020\pi$
$230$	3.38868			0.223443
$231$	14.9669	+	2.64441i	0.984748	+	0.173989i
$232$	0.663414			0.0435553
$233$	15.6399	+	5.08170i	1.02460	+	0.332913i	0.772654	−	0.634827i	$-0.218929\pi$
$233$	15.6399	+	5.08170i	1.02460	+	0.332913i	0.251948	+	0.967741i	$0.418929\pi$
$234$	12.1916	−	2.94630i	0.796992	−	0.192606i
$235$	2.37271	+	1.72388i	0.154779	+	0.112453i
$236$	−2.62272	−	8.07189i	−0.170724	−	0.525435i
$237$	1.30185	+	10.9290i	0.0845640	+	0.709915i
$238$	5.74040	−	1.52243i	0.372095	−	0.0986845i
$239$	−6.31195	−	8.68766i	−0.408286	−	0.561958i	0.554513	−	0.832175i	$-0.312905\pi$
$239$	−6.31195	−	8.68766i	−0.408286	−	0.561958i	−0.962799	+	0.270217i	$0.912905\pi$
$240$	1.33981	−	2.39662i	0.0864845	−	0.154701i
$241$			18.1478i			1.16900i	0.811392	+	0.584502i	$0.198710\pi$
$241$			18.1478i			1.16900i	−0.811392	+	0.584502i	$0.801290\pi$
$242$	3.22158	−	6.23290i	0.207091	−	0.400666i
$243$	−8.70903	−	12.9288i	−0.558685	−	0.829380i
$244$	−5.07703	−	1.64963i	−0.325023	−	0.105607i
$245$	4.75990	+	4.33007i	0.304099	+	0.276638i
$246$	6.52097	−	6.03700i	0.415762	−	0.384905i
$247$	−0.294513	−	0.906417i	−0.0187394	−	0.0576739i
$248$	2.91743	+	8.97894i	0.185257	+	0.570163i
$249$	17.6056	+	19.0170i	1.11571	+	1.20516i
$250$	−3.15516	−	4.34271i	−0.199550	−	0.274657i
$251$	−2.67412	+	8.23010i	−0.168789	+	0.519479i	−0.999296	−	0.0375296i	$-0.988051\pi$
$251$	−2.67412	+	8.23010i	−0.168789	+	0.519479i	0.830506	+	0.557009i	$0.188051\pi$
$252$	6.02211	+	11.1193i	0.379357	+	0.700449i
$253$	−12.4064	−	14.6117i	−0.779981	−	0.918631i
$254$		−	9.84801i		−	0.617919i
$255$	2.73418	−	4.89083i	0.171221	−	0.306276i
$256$	6.09304	−	4.42685i	0.380815	−	0.276678i
$257$	−5.40022	−	3.92349i	−0.336856	−	0.244741i	0.406478	−	0.913661i	$-0.366757\pi$
$257$	−5.40022	−	3.92349i	−0.336856	−	0.244741i	−0.743334	+	0.668920i	$0.766757\pi$
$258$	4.15517	−	0.494958i	0.258690	−	0.0308147i
$259$	−1.84521	+	4.77048i	−0.114656	+	0.296423i
$260$	−5.64244	+	7.76616i	−0.349929	+	0.481637i
$261$	0.203990	+	0.844097i	0.0126266	+	0.0522483i
$262$	5.51315	+	1.79133i	0.340604	+	0.110669i
$263$		−	13.5884i		−	0.837898i	−0.908010	−	0.418949i	$-0.862399\pi$
$263$		−	13.5884i		−	0.837898i	0.908010	−	0.418949i	$-0.137601\pi$
$264$	12.9183	−	2.54067i	0.795064	−	0.156367i
$265$			10.3691i			0.636969i
$266$	−0.206128	+	0.133114i	−0.0126385	+	0.00816174i
$267$	−22.4181	+	10.3553i	−1.37197	+	0.633734i
$268$	7.60881	+	5.52812i	0.464782	+	0.337684i
$269$	6.04648	+	18.6092i	0.368660	+	1.13462i	0.947657	+	0.319290i	$0.103444\pi$
$269$	6.04648	+	18.6092i	0.368660	+	1.13462i	−0.578997	+	0.815330i	$0.696556\pi$
$270$	−2.93415	−	0.820393i	−0.178567	−	0.0499275i
$271$	−4.93000	+	6.78556i	−0.299476	+	0.412194i	−0.932063	−	0.362296i	$-0.881993\pi$
$271$	−4.93000	+	6.78556i	−0.299476	+	0.412194i	0.632587	+	0.774489i	$0.281993\pi$
$272$	−4.90974	+	3.56713i	−0.297697	+	0.216289i
$273$	−11.0803	−	27.9192i	−0.670609	−	1.68975i
$274$	−6.37935			−0.385391
$275$	−3.25591	+	13.3903i	−0.196339	+	0.807468i
$276$	3.09956	−	15.6439i	0.186572	−	0.941650i
$277$	3.05926	−	9.41544i	0.183813	−	0.565719i	−0.816113	−	0.577893i	$-0.803875\pi$
$277$	3.05926	−	9.41544i	0.183813	−	0.565719i	0.999926	+	0.0121738i	$0.00387513\pi$
$278$	−1.26396	+	0.918324i	−0.0758075	+	0.0550774i
$279$	−10.5273	+	6.47289i	−0.630254	+	0.387522i
$280$	5.19871	+	2.01085i	0.310682	+	0.120171i
$281$	−19.4410	+	6.31675i	−1.15975	+	0.376826i	−0.824808	−	0.565413i	$-0.808717\pi$
$281$	−19.4410	+	6.31675i	−1.15975	+	0.376826i	−0.334942	+	0.942239i	$0.608717\pi$
$282$	−2.58649	+	2.39453i	−0.154023	+	0.142592i
$283$	11.4365	+	15.7410i	0.679830	+	0.935706i	0.999932	−	0.0116772i	$-0.00371705\pi$
$283$	11.4365	+	15.7410i	0.679830	+	0.935706i	−0.320102	+	0.947383i	$0.603717\pi$
$284$	9.09883	+	2.95639i	0.539916	+	0.175429i
$285$	−0.0449942	+	0.227091i	−0.00266523	+	0.0134517i
$286$	−13.8267	+	1.04777i	−0.817591	+	0.0619560i
$287$	−16.5046	−	13.4351i	−0.974237	−	0.793050i
$288$	12.9823	+	11.0543i	0.764988	+	0.651379i
$289$	3.73390	−	2.71284i	0.219641	−	0.159579i
$290$	0.137309	+	0.0997611i	0.00806308	+	0.00585817i
$291$	24.0974	−	2.87045i	1.41261	−	0.168268i
$292$	12.6325	−	4.10454i	0.739260	−	0.240200i
$293$	−10.8486	−	7.88194i	−0.633780	−	0.460468i	0.223928	−	0.974606i	$-0.428112\pi$
$293$	−10.8486	−	7.88194i	−0.633780	−	0.460468i	−0.857708	+	0.514138i	$0.828112\pi$
$294$	−6.21652	+	4.60003i	−0.362555	+	0.268279i
$295$	1.51330	−	4.65747i	0.0881080	−	0.271168i
$296$			4.43075i			0.257532i
$297$	7.20479	+	15.6554i	0.418065	+	0.908417i
$298$	6.74668			0.390825
$299$	−11.7064	+	36.0285i	−0.676997	+	2.08358i
$300$	−10.4086	+	4.80791i	−0.600941	+	0.277585i
$301$	−2.56898	−	9.68646i	−0.148073	−	0.558318i
$302$	−9.34988	+	3.03796i	−0.538025	+	0.174815i
$303$	−2.63359	−	22.1090i	−0.151296	−	1.27013i
$304$	0.147382	−	0.202854i	0.00845294	−	0.0116345i
$305$	−1.81049	−	2.49193i	−0.103668	−	0.142687i
$306$	5.12715	+	4.36571i	0.293099	+	0.249571i
$307$		−	23.0285i		−	1.31430i	−0.753758	−	0.657152i	$-0.771761\pi$
$307$		−	23.0285i		−	1.31430i	0.753758	−	0.657152i	$-0.228239\pi$
$308$	−4.59458	−	13.2033i	−0.261800	−	0.752330i
$309$	2.04993	−	10.3462i	0.116616	−	0.588576i
$310$	−0.746378	+	2.29711i	−0.0423914	+	0.130467i
$311$	22.7672	−	16.5414i	1.29101	−	0.937975i	0.291186	−	0.956666i	$-0.405950\pi$
$311$	22.7672	−	16.5414i	1.29101	−	0.937975i	0.999825	+	0.0186916i	$0.00595006\pi$
$312$	−17.6766	−	19.0936i	−1.00074	−	1.08096i
$313$	12.7112	−	4.13013i	0.718482	−	0.233449i	0.0731170	−	0.997323i	$-0.476705\pi$
$313$	12.7112	−	4.13013i	0.718482	−	0.233449i	0.645365	+	0.763874i	$0.276705\pi$
$314$	0.304956	+	0.938559i	0.0172097	+	0.0529660i
$315$	−0.959987	+	7.23290i	−0.0540892	+	0.407528i
$316$	8.19024	−	5.95056i	0.460737	−	0.334745i
$317$	−15.9452	−	5.18091i	−0.895572	−	0.290989i	−0.175164	−	0.984539i	$-0.556046\pi$
$317$	−15.9452	−	5.18091i	−0.895572	−	0.290989i	−0.720408	+	0.693550i	$0.756046\pi$
$318$	−12.2241	−	2.42200i	−0.685495	−	0.135819i
$319$	−0.0725433	−	0.957303i	−0.00406164	−	0.0535987i
$320$	0.162065			0.00905969
$321$	−14.5527	−	8.13560i	−0.812255	−	0.454085i
$322$	9.73846	+	0.535318i	0.542703	+	0.0298321i
$323$	0.300765	−	0.413968i	0.0167350	−	0.0230338i
$324$	−6.47116	+	12.7951i	−0.359509	+	0.710840i
$325$	25.9018	−	8.41600i	1.43677	−	0.466835i
$326$	−6.22132	+	8.56291i	−0.344567	+	0.474256i
$327$	1.92492	−	0.889154i	0.106449	−	0.0491703i
$328$	−17.5327	−	5.69672i	−0.968082	−	0.314549i
$329$	6.54642	+	5.32893i	0.360916	+	0.293794i
$330$	3.05580	+	1.41674i	0.168216	+	0.0779887i
$331$	5.06225			0.278246			0.139123	−	0.990275i	$-0.455572\pi$
$331$	5.06225			0.278246			0.139123	+	0.990275i	$0.455572\pi$
$332$	7.36612	−	22.6706i	0.404268	−	1.24421i
$333$	−5.63747	+	1.36239i	−0.308932	+	0.0746583i
$334$	0.650213	−	0.894941i	0.0355781	−	0.0489690i
$335$	1.67693	+	5.16107i	0.0916207	+	0.281979i
$336$	4.22898	−	6.67580i	0.230710	−	0.364195i
$337$	−4.01931	−	2.92020i	−0.218946	−	0.159073i	0.472906	−	0.881113i	$-0.343205\pi$
$337$	−4.01931	−	2.92020i	−0.218946	−	0.159073i	−0.691852	+	0.722039i	$0.743205\pi$
$338$	11.2340	+	15.4623i	0.611052	+	0.841040i
$339$	17.2231	+	9.62844i	0.935431	+	0.522945i
$340$	−5.15390			−0.279509
$341$	12.6375	−	5.19168i	0.684362	−	0.281145i
$342$	−0.257208	−	0.106087i	−0.0139082	−	0.00573654i
$343$	12.9951	+	13.1958i	0.701668	+	0.712504i
$344$	−5.10250	−	7.02299i	−0.275109	−	0.378654i
$345$	6.75251	−	6.25136i	0.363543	−	0.336562i
$346$	6.88990	−	2.23867i	0.370403	−	0.120351i
$347$	−12.5410	+	4.07482i	−0.673236	+	0.218748i	−0.625631	−	0.780119i	$-0.715159\pi$
$347$	−12.5410	+	4.07482i	−0.673236	+	0.218748i	−0.0476042	+	0.998866i	$0.515159\pi$
$348$	0.586141	−	0.542639i	0.0314205	−	0.0290885i
$349$	−3.45539	−	4.75594i	−0.184963	−	0.254580i	0.706459	−	0.707754i	$-0.250291\pi$
$349$	−3.45539	−	4.75594i	−0.184963	−	0.254580i	−0.891422	+	0.453174i	$0.850291\pi$
$350$	−3.80386	−	5.89032i	−0.203325	−	0.314851i
$351$	18.8586	−	28.3618i	1.00660	−	1.51384i
$352$	−12.2008	−	14.3696i	−0.650303	−	0.765902i
$353$	32.9898			1.75587			0.877934	−	0.478782i	$-0.158921\pi$
$353$	32.9898			1.75587			0.877934	+	0.478782i	$0.158921\pi$
$354$	5.13721	+	2.87192i	0.273040	+	0.152641i
$355$	3.24469	+	4.46593i	0.172210	+	0.237027i
$356$	18.3760	+	13.3510i	0.973928	+	0.707600i
$357$	8.63015	−	13.6234i	0.456756	−	0.721029i
$358$	−3.49632	−	10.7606i	−0.184786	−	0.568714i
$359$	−6.14880	+	8.46309i	−0.324521	+	0.446665i	−0.939841	−	0.341613i	$-0.889027\pi$
$359$	−6.14880	+	8.46309i	−0.324521	+	0.446665i	0.615320	+	0.788278i	$0.289027\pi$
$360$	1.48468	+	6.14353i	0.0782497	+	0.323793i
$361$	5.86479	−	18.0500i	0.308673	−	0.949998i
$362$	−6.02306			−0.316565
$363$	−5.07876	−	18.3632i	−0.266566	−	0.963817i
$364$	−17.4422	+	21.4272i	−0.914220	+	1.12309i
$365$	7.28892	+	2.36831i	0.381520	+	0.123963i
$366$	3.36062	−	1.55233i	0.175663	−	0.0811414i
$367$	3.55352	−	4.89101i	0.185492	−	0.255308i	−0.706136	−	0.708076i	$-0.749563\pi$
$367$	3.55352	−	4.89101i	0.185492	−	0.255308i	0.891628	+	0.452768i	$0.149563\pi$
$368$	−9.47873	+	3.07983i	−0.494113	+	0.160547i
$369$	1.85721	−	24.0595i	0.0966824	−	1.25249i
$370$	−0.666274	+	0.917048i	−0.0346380	+	0.0476751i
$371$	−1.63803	+	29.7989i	−0.0850423	+	1.54708i
$372$	9.92194	+	5.54678i	0.514429	+	0.287587i
$373$	6.05085			0.313301			0.156651	−	0.987654i	$-0.449930\pi$
$373$	6.05085			0.313301			0.156651	+	0.987654i	$0.449930\pi$
$374$	−4.81850	−	5.67505i	−0.249159	−	0.293450i
$375$	−14.2985	−	2.83300i	−0.738372	−	0.146296i
$376$	6.95421	+	2.25956i	0.358636	+	0.116528i
$377$	−1.53500	+	1.11524i	−0.0790566	+	0.0574380i
$378$	−8.30263	−	2.82118i	−0.427041	−	0.145106i
$379$	1.38172	+	4.25249i	0.0709741	+	0.218436i	0.980252	−	0.197755i	$-0.0633650\pi$
$379$	1.38172	+	4.25249i	0.0709741	+	0.218436i	−0.909277	+	0.416190i	$0.863365\pi$
$380$	0.202520	−	0.0658027i	0.0103890	−	0.00337561i
$381$	−18.1674	−	19.6238i	−0.930743	−	1.00536i
$382$	0.840801	−	0.610878i	0.0430191	−	0.0312552i
$383$	5.53451	−	17.0335i	0.282800	−	0.870370i	−0.704249	−	0.709953i	$-0.748716\pi$
$383$	5.53451	−	17.0335i	0.282800	−	0.870370i	0.987049	−	0.160417i	$-0.0512839\pi$
$384$	3.78875	−	19.1223i	0.193344	−	0.975830i
$385$	2.33317	−	7.72160i	0.118910	−	0.393529i
$386$			7.02445i			0.357535i
$387$	7.36679	−	8.65165i	0.374475	−	0.439788i
$388$	−13.1204	−	18.0587i	−0.666088	−	0.916791i
$389$	−12.2732	+	16.8927i	−0.622278	+	0.856493i	−0.997516	−	0.0704358i	$-0.977561\pi$
$389$	−12.2732	+	16.8927i	−0.622278	+	0.856493i	0.375238	+	0.926929i	$0.377561\pi$
$390$	−0.787373	−	6.61000i	−0.0398702	−	0.334710i
$391$	−19.3434	+	6.28506i	−0.978239	+	0.317849i
$392$	14.6225	+	6.60007i	0.738548	+	0.333354i
$393$	14.2905	−	6.60100i	0.720859	−	0.332976i
$394$	−0.119793	+	0.368685i	−0.00603509	+	0.0185741i
$395$	5.84136			0.293910
$396$	9.33544	−	12.8112i	0.469123	−	0.643788i
$397$		−	28.1638i		−	1.41350i	−0.707463	−	0.706750i	$-0.750161\pi$
$397$		−	28.1638i		−	1.41350i	0.707463	−	0.706750i	$-0.249839\pi$
$398$	−1.18327	+	3.64172i	−0.0593117	+	0.182543i
$399$	−0.165179	+	0.645512i	−0.00826932	+	0.0323160i
$400$	5.79676	+	4.21159i	0.289838	+	0.210579i
$401$	22.6951	−	7.37408i	1.13334	−	0.368244i	0.318495	−	0.947925i	$-0.396823\pi$
$401$	22.6951	−	7.37408i	1.13334	−	0.368244i	0.814844	+	0.579680i	$0.196823\pi$
$402$	−6.47607	+	0.771420i	−0.322997	+	0.0384749i
$403$	−21.8445	−	15.8710i	−1.08815	−	0.790590i
$404$	−16.5686	+	12.0378i	−0.824318	+	0.598902i
$405$	−7.36023	+	3.77808i	−0.365733	+	0.187734i
$406$	0.378843	+	0.308386i	0.0188017	+	0.0153050i
$407$	6.39354	−	0.484495i	0.316916	−	0.0240155i
$408$	2.71510	−	13.7034i	0.134417	−	0.678421i
$409$	28.3115	+	9.19898i	1.39992	+	0.454860i	0.909164	−	0.416439i	$-0.136722\pi$
$409$	28.3115	+	9.19898i	1.39992	+	0.454860i	0.490752	+	0.871299i	$0.336722\pi$
$410$	−2.77217	−	3.81556i	−0.136907	−	0.188437i
$411$	−12.7119	+	11.7685i	−0.627033	+	0.580496i
$412$	−9.22675	+	2.99795i	−0.454569	+	0.147699i
$413$	5.08471	−	13.1457i	0.250202	−	0.646856i
$414$	5.79248	+	9.42071i	0.284685	+	0.463003i
$415$	11.1273	−	8.08443i	0.546216	−	0.396849i
$416$	−11.5124	+	35.4315i	−0.564441	+	1.73717i
$417$	−0.824558	+	4.16164i	−0.0403788	+	0.203797i
$418$	0.261797	+	0.161478i	0.0128049	+	0.00789813i
$419$	18.1645			0.887396			0.443698	−	0.896176i	$-0.353666\pi$
$419$	18.1645			0.887396			0.443698	+	0.896176i	$0.353666\pi$
$420$	6.23795	−	2.47565i	0.304381	−	0.120800i
$421$	−6.12058	+	4.44686i	−0.298299	+	0.216727i	−0.726859	−	0.686786i	$-0.759021\pi$
$421$	−6.12058	+	4.44686i	−0.298299	+	0.216727i	0.428561	+	0.903513i	$0.359021\pi$
$422$	−6.49416	+	8.93844i	−0.316131	+	0.435117i
$423$	−0.736646	+	9.54299i	−0.0358170	+	0.463996i
$424$	7.98873	+	24.5868i	0.387967	+	1.19404i
$425$	11.8295	+	8.59467i	0.573817	+	0.416903i
$426$	−6.02276	+	2.78201i	−0.291804	+	0.134789i
$427$	−4.80937	−	7.44736i	−0.232742	−	0.360403i
$428$			15.3355i			0.741270i
$429$	−25.6191	+	27.5950i	−1.23690	+	1.33230i
$430$		−	2.22087i		−	0.107100i
$431$	4.85847	+	1.57861i	0.234024	+	0.0760390i	0.423681	−	0.905811i	$-0.360738\pi$
$431$	4.85847	+	1.57861i	0.234024	+	0.0760390i	−0.189657	+	0.981850i	$0.560738\pi$
$432$	8.95295	−	0.371942i	0.430749	−	0.0178951i
$433$	−10.5750	+	14.5553i	−0.508204	+	0.699483i	−0.983615	−	0.180281i	$-0.942299\pi$
$433$	−10.5750	+	14.5553i	−0.508204	+	0.699483i	0.475411	+	0.879764i	$0.342299\pi$
$434$	−2.50784	+	6.48359i	−0.120380	+	0.311222i
$435$	0.457648	−	0.0545144i	0.0219426	−	0.00261376i
$436$	−1.57785	−	1.14638i	−0.0755654	−	0.0549015i
$437$	0.679845	−	0.493936i	0.0325214	−	0.0236282i
$438$	−4.49454	+	8.03971i	−0.214757	+	0.384152i
$439$			20.7576i			0.990705i	0.868692	+	0.495352i	$0.164961\pi$
$439$			20.7576i			0.990705i	−0.868692	+	0.495352i	$0.835039\pi$
$440$	−0.527987	−	6.96747i	−0.0251708	−	0.332161i
$441$	−3.90143	+	20.6344i	−0.185782	+	0.982591i
$442$	−4.54664	+	13.9931i	−0.216261	+	0.665584i
$443$	−14.7819	−	20.3456i	−0.702311	−	0.966649i	−0.999928	−	0.0119635i	$-0.996192\pi$
$443$	−14.7819	−	20.3456i	−0.702311	−	0.966649i	0.297617	−	0.954685i	$-0.403808\pi$
$444$	3.62413	+	3.91466i	0.171993	+	0.185782i
$445$	4.04997	+	12.4645i	0.191987	+	0.590875i
$446$	−4.23710	−	13.0404i	−0.200632	−	0.617483i
$447$	13.4439	−	12.4461i	0.635874	−	0.588681i
$448$	0.465745	+	0.0256017i	0.0220044	+	0.00120957i
$449$	−0.846360	−	0.274999i	−0.0399422	−	0.0129780i	0.288978	−	0.957336i	$-0.406685\pi$
$449$	−0.846360	−	0.274999i	−0.0399422	−	0.0129780i	−0.328920	+	0.944358i	$0.606685\pi$
$450$	3.03155	−	7.34998i	0.142909	−	0.346481i
$451$	−6.30317	+	25.9225i	−0.296805	+	1.22064i
$452$		−	18.1495i		−	0.853681i
$453$	−13.0268	+	23.3021i	−0.612054	+	1.09483i
$454$	−6.08598	−	8.37664i	−0.285629	−	0.393135i
$455$	−15.4091	+	4.08670i	−0.722390	+	0.191587i
$456$	0.0682709	+	0.573134i	0.00319708	+	0.0268395i
$457$	5.47067	+	16.8370i	0.255907	+	0.787601i	0.993650	+	0.112519i	$0.0358918\pi$
$457$	5.47067	+	16.8370i	0.255907	+	0.787601i	−0.737743	+	0.675082i	$0.764108\pi$
$458$	−13.2132	−	9.59995i	−0.617412	−	0.448576i
$459$	18.2705	−	0.759029i	0.852792	−	0.0354284i
$460$	−8.04980	−	2.61554i	−0.375324	−	0.121950i
$461$	7.83221			0.364782			0.182391	−	0.983226i	$-0.441616\pi$
$461$	7.83221			0.364782			0.182391	+	0.983226i	$0.441616\pi$
$462$	8.55800	+	4.55417i	0.398154	+	0.211879i
$463$	2.81171			0.130671			0.0653356	−	0.997863i	$-0.479188\pi$
$463$	2.81171			0.130671			0.0653356	+	0.997863i	$0.479188\pi$
$464$	−0.474746	−	0.154254i	−0.0220395	−	0.00716108i
$465$	2.75038	+	5.95428i	0.127546	+	0.276123i
$466$	8.48586	+	6.16534i	0.393100	+	0.285604i
$467$	−2.79987	−	8.61713i	−0.129563	−	0.398753i	0.865142	−	0.501527i	$-0.167228\pi$
$467$	−2.79987	−	8.61713i	−0.129563	−	0.398753i	−0.994705	+	0.102774i	$0.967228\pi$
$468$	−31.2353	−	2.41113i	−1.44385	−	0.111454i
$469$	4.00390	+	15.0969i	0.184883	+	0.697110i
$470$	1.09956	+	1.51341i	0.0507188	+	0.0698084i
$471$	2.33911	+	1.30766i	0.107780	+	0.0602538i
$472$		−	12.2095i		−	0.561987i
$473$	−9.57620	+	8.13084i	−0.440314	+	0.373857i
$474$	−1.36441	+	6.88636i	−0.0626696	+	0.316301i
$475$	−0.574569	−	0.186689i	−0.0263630	−	0.00856587i
$476$	−14.8114	−	0.814173i	−0.678878	−	0.0373175i
$477$	−28.8266	+	17.7245i	−1.31988	+	0.811551i
$478$	−2.11660	−	6.51423i	−0.0968111	−	0.297954i
$479$	0.625063	+	1.92375i	0.0285599	+	0.0878982i	0.964320	−	0.264738i	$-0.0852854\pi$
$479$	0.625063	+	1.92375i	0.0285599	+	0.0878982i	−0.935761	+	0.352636i	$0.885285\pi$
$480$	6.64062	−	6.14777i	0.303102	−	0.280606i
$481$	−7.44838	−	10.2518i	−0.339617	−	0.467443i
$482$	−3.57699	+	11.0089i	−0.162928	+	0.501440i
$483$	20.3931	−	16.8986i	0.927916	−	0.768912i
$484$	−12.4637	+	12.3197i	−0.566531	+	0.559985i
$485$		−	12.8796i		−	0.584834i
$486$	−2.73479	−	9.55944i	−0.124052	−	0.433625i
$487$	19.0912	−	13.8706i	0.865106	−	0.628536i	−0.0641633	−	0.997939i	$-0.520438\pi$
$487$	19.0912	−	13.8706i	0.865106	−	0.628536i	0.929269	+	0.369403i	$0.120438\pi$
$488$	−6.21283	−	4.51388i	−0.281242	−	0.204334i
$489$	3.39964	+	28.5400i	0.153737	+	1.29062i
$490$	2.03399	+	3.56490i	0.0918862	+	0.161046i
$491$	2.22240	−	3.05887i	0.100295	−	0.138045i	−0.755920	−	0.654664i	$-0.772810\pi$
$491$	2.22240	−	3.05887i	0.100295	−	0.138045i	0.856215	+	0.516620i	$0.172810\pi$
$492$	−20.1502	+	9.30769i	−0.908440	+	0.419623i
$493$	−0.968824	−	0.314790i	−0.0436336	−	0.0141774i
$494$		−	0.607901i		−	0.0273508i
$495$	8.70274	−	2.81418i	0.391159	−	0.126488i
$496$		−	7.10378i		−	0.318969i
$497$	8.61915	+	13.3468i	0.386622	+	0.598688i
$498$	6.93164	+	15.0063i	0.310614	+	0.672447i
$499$	−12.2622	−	8.90903i	−0.548933	−	0.398823i	0.278459	−	0.960448i	$-0.410176\pi$
$499$	−12.2622	−	8.90903i	−0.548933	−	0.398823i	−0.827392	+	0.561625i	$0.810176\pi$
$500$	4.14318	+	12.7514i	0.185289	+	0.570259i
$501$	−0.355309	−	2.98282i	−0.0158740	−	0.133262i
$502$	−3.24436	+	4.46548i	−0.144803	+	0.199304i
$503$	−7.23058	+	5.25332i	−0.322396	+	0.234234i	−0.737197	−	0.675678i	$-0.763851\pi$
$503$	−7.23058	+	5.25332i	−0.322396	+	0.234234i	0.414801	+	0.909912i	$0.363851\pi$
$504$	3.29620	+	17.8899i	0.146825	+	0.796882i
$505$	−11.8169			−0.525844
$506$	−4.64594	−	11.3091i	−0.206537	−	0.502752i
$507$	50.9103	+	10.0870i	2.26100	+	0.447979i
$508$	−7.60115	+	23.3939i	−0.337246	+	1.03794i
$509$	−8.31132	+	6.03853i	−0.368393	+	0.267653i	−0.756544	−	0.653943i	$-0.773114\pi$
$509$	−8.31132	+	6.03853i	−0.368393	+	0.267653i	0.388151	+	0.921596i	$0.373114\pi$
$510$	2.62261	−	2.42797i	0.116131	−	0.107512i
$511$	20.5729	+	7.95756i	0.910092	+	0.352022i
$512$	−16.8393	+	5.47143i	−0.744200	+	0.241805i
$513$	−0.708237	+	0.263095i	−0.0312694	+	0.0116159i
$514$	−2.50256	−	3.44447i	−0.110383	−	0.151929i
$515$	−5.32382	−	1.72981i	−0.234596	−	0.0762247i
$516$	−10.2526	−	2.03138i	−0.451347	−	0.0894266i
$517$	2.50010	−	10.2820i	0.109954	−	0.452200i
$518$	−2.05962	+	2.53018i	−0.0904945	+	0.111170i
$519$	9.59944	−	17.1712i	0.421369	−	0.753734i
$520$	−11.1721	+	8.11700i	−0.489929	+	0.355954i
$521$	−17.9055	−	13.0091i	−0.784455	−	0.569940i	0.121858	−	0.992548i	$-0.461115\pi$
$521$	−17.9055	−	13.0091i	−0.784455	−	0.569940i	−0.906313	+	0.422608i	$0.861115\pi$
$522$	−0.0426299	+	0.552254i	−0.00186586	+	0.0241715i
$523$	−3.93171	+	1.27749i	−0.171922	+	0.0558608i	−0.393713	−	0.919233i	$-0.628810\pi$
$523$	−3.93171	+	1.27749i	−0.171922	+	0.0558608i	0.221791	+	0.975094i	$0.428810\pi$
$524$	−11.7138	−	8.51060i	−0.511722	−	0.371787i
$525$	−18.4462	−	4.72017i	−0.805056	−	0.206005i
$526$	2.67832	−	8.24303i	0.116780	−	0.359413i
$527$		−	14.4968i		−	0.631491i
$528$	−9.83520	−	1.18557i	−0.428022	−	0.0515955i
$529$	−10.4018			−0.452253
$530$	−2.04378	+	6.29012i	−0.0887763	+	0.273225i
$531$	15.5348	−	3.75423i	0.674152	−	0.162920i
$532$	0.592400	−	0.157112i	0.0256838	−	0.00681169i
$533$	50.1436	−	16.2926i	2.17196	−	0.705713i
$534$	−15.6404	+	1.86306i	−0.676826	+	0.0806224i
$535$	−5.20106	+	7.15864i	−0.224861	+	0.309495i
$536$	7.95254	+	10.9457i	0.343498	+	0.472784i
$537$	−26.8179	−	14.9923i	−1.15728	−	0.646966i
$538$			12.4805i			0.538072i
$539$	7.92492	−	21.8219i	0.341351	−	0.939936i
$540$	6.33685	+	4.21355i	0.272695	+	0.181322i
$541$	−5.38295	+	16.5670i	−0.231431	+	0.712271i	0.766144	+	0.642669i	$0.222173\pi$
$541$	−5.38295	+	16.5670i	−0.231431	+	0.712271i	−0.997575	+	0.0696021i	$0.977827\pi$
$542$	−4.32810	+	3.14455i	−0.185908	+	0.135070i
$543$	−12.0020	+	11.1112i	−0.515053	+	0.476827i
$544$	−19.0229	+	6.18091i	−0.815600	+	0.265004i
$545$	−0.347749	−	1.07026i	−0.0148959	−	0.0458449i
$546$	−1.21857	−	19.1203i	−0.0521501	−	0.818275i
$547$	2.04406	−	1.48510i	0.0873977	−	0.0634982i	−0.543228	−	0.839585i	$-0.682798\pi$
$547$	2.04406	−	1.48510i	0.0873977	−	0.0634982i	0.630626	+	0.776087i	$0.282798\pi$
$548$	15.1541	+	4.92387i	0.647352	+	0.210338i
$549$	3.83291	−	9.29286i	0.163585	−	0.396610i
$550$	−4.61439	+	7.48112i	−0.196758	+	0.318996i
$551$	0.0420885			0.00179303
$552$	11.1950	−	20.0253i	0.476491	−	0.852334i
$553$	16.7870	+	0.922772i	0.713856	+	0.0392403i
$554$	3.71163	−	5.10862i	0.157692	−	0.217044i
$555$	0.364085	+	3.05650i	0.0154546	+	0.129741i
$556$	3.71135	−	1.20589i	0.157396	−	0.0511411i
$557$	10.6879	−	14.7106i	0.452860	−	0.623309i	−0.520149	−	0.854076i	$-0.674123\pi$
$557$	10.6879	−	14.7106i	0.452860	−	0.623309i	0.973009	+	0.230767i	$0.0741235\pi$
$558$	−7.66192	+	1.85163i	−0.324355	+	0.0783856i
$559$	23.6123	+	7.67209i	0.998692	+	0.324495i
$560$	−3.25270	−	2.64777i	−0.137452	−	0.111889i
$561$	−20.0709	−	2.41942i	−0.847393	−	0.102148i
$562$	−13.0383			−0.549990
$563$	4.74436	−	14.6017i	0.199951	−	0.615386i	−0.799932	−	0.600091i	$-0.795131\pi$
$563$	4.74436	−	14.6017i	0.199951	−	0.615386i	0.999883	−	0.0152955i	$-0.00486890\pi$
$564$	7.99240	−	3.69182i	0.336541	−	0.155454i
$565$	6.15543	−	8.47222i	0.258961	−	0.356429i
$566$	3.83503	+	11.8030i	0.161198	+	0.496118i
$567$	−21.7488	+	9.69482i	−0.913364	+	0.407144i
$568$	11.1344	+	8.08959i	0.467188	+	0.339432i
$569$	−12.9845	−	17.8717i	−0.544340	−	0.749220i	0.444890	−	0.895585i	$-0.353243\pi$
$569$	−12.9845	−	17.8717i	−0.544340	−	0.749220i	−0.989231	+	0.146365i	$0.953243\pi$
$570$	−0.0720549	+	0.128890i	−0.00301805	+	0.00539861i
$571$	18.4614			0.772586			0.386293	−	0.922376i	$-0.373755\pi$
$571$	18.4614			0.772586			0.386293	+	0.922376i	$0.373755\pi$
$572$	33.6540	+	8.18311i	1.40715	+	0.342153i
$573$	0.548504	−	2.76837i	0.0229141	−	0.115650i
$574$	−7.36395	−	11.4032i	−0.307365	−	0.475958i
$575$	14.1147	+	19.4273i	0.588625	+	0.810172i
$576$	0.277027	+	0.450548i	0.0115428	+	0.0187728i
$577$	−16.0183	+	5.20467i	−0.666851	+	0.216673i	−0.622830	−	0.782357i	$-0.714017\pi$
$577$	−16.0183	+	5.20467i	−0.666851	+	0.216673i	−0.0440217	+	0.999031i	$0.514017\pi$
$578$	2.79977	−	0.909701i	0.116455	−	0.0378386i
$579$	12.9585	+	13.9974i	0.538538	+	0.581712i
$580$	−0.249178	−	0.342964i	−0.0103465	−	0.0142408i
$581$	33.2549	−	21.4754i	1.37965	−	0.890950i
$582$	15.1838	+	3.00840i	0.629388	+	0.124702i
$583$	34.6050	−	14.2162i	1.43319	−	0.588776i
$584$	19.1078			0.790687
$585$	−13.7629	−	11.7190i	−0.569028	−	0.484521i
$586$	−5.02742	−	6.91964i	−0.207681	−	0.285848i
$587$	−37.3494	−	27.1359i	−1.54158	−	1.12002i	−0.949338	−	0.314257i	$-0.898245\pi$
$587$	−37.3494	−	27.1359i	−1.54158	−	1.12002i	−0.592238	−	0.805763i	$-0.701755\pi$
$588$	18.3178	−	6.12916i	0.755415	−	0.252762i
$589$	0.185089	+	0.569645i	0.00762645	+	0.0234718i
$590$	1.83601	−	2.52704i	0.0755871	−	0.104037i
$591$	0.441434	+	0.955658i	0.0181582	+	0.0393105i
$592$	1.03022	−	3.17069i	0.0423418	−	0.130315i
$593$	−1.74812			−0.0717866			−0.0358933	−	0.999356i	$-0.511428\pi$
$593$	−1.74812			−0.0717866			−0.0358933	+	0.999356i	$0.511428\pi$
$594$	1.28486	+	10.9170i	0.0527183	+	0.447929i
$595$	−6.63784	−	5.40335i	−0.272125	−	0.221516i
$596$	−16.0267	−	5.20740i	−0.656480	−	0.213303i
$597$	4.36030	+	9.43959i	0.178455	+	0.386337i
$598$	−14.2027	+	19.5483i	−0.580790	+	0.799389i
$599$	6.97933	−	2.26772i	0.285168	−	0.0926566i	−0.162941	−	0.986636i	$-0.552098\pi$
$599$	6.97933	−	2.26772i	0.285168	−	0.0926566i	0.448108	+	0.893979i	$0.352098\pi$
$600$	−16.3779	+	1.95091i	−0.668624	+	0.0796455i
$601$	−15.7217	+	21.6390i	−0.641300	+	0.882674i	−0.998684	−	0.0512838i	$-0.983669\pi$
$601$	−15.7217	+	21.6390i	−0.641300	+	0.882674i	0.357384	+	0.933957i	$0.383669\pi$
$602$	0.350835	−	6.38237i	0.0142990	−	0.260126i
$603$	−11.4816	+	13.4841i	−0.467565	+	0.549115i
$604$	24.5554			0.999147
$605$	−9.99630	+	1.52376i	−0.406407	+	0.0619498i
$606$	2.76017	−	13.9309i	0.112124	−	0.565904i
$607$	18.8295	+	6.11807i	0.764265	+	0.248325i	0.665108	−	0.746747i	$-0.268385\pi$
$607$	18.8295	+	6.11807i	0.764265	+	0.248325i	0.0991571	+	0.995072i	$0.468385\pi$
$608$	0.668580	−	0.485752i	0.0271145	−	0.0196998i
$609$	1.32381	−	0.0843688i	0.0536435	−	0.00341879i
$610$	−0.607116	−	1.86851i	−0.0245814	−	0.0756538i
$611$	−19.8891	+	6.46234i	−0.804625	+	0.261438i
$612$	−8.80986	−	14.3281i	−0.356118	−	0.579179i
$613$	−33.2953	+	24.1904i	−1.34478	+	0.977042i	−0.345530	+	0.938408i	$0.612301\pi$
$613$	−33.2953	+	24.1904i	−1.34478	+	0.977042i	−0.999253	+	0.0386344i	$0.987699\pi$
$614$	4.53899	−	13.9696i	0.183179	−	0.563766i
$615$	−12.5629	−	2.48911i	−0.506583	−	0.100371i
$616$	−0.416671	−	20.1067i	−0.0167882	−	0.810121i
$617$		−	39.5281i		−	1.59134i	−0.605728	−	0.795672i	$-0.707118\pi$
$617$		−	39.5281i		−	1.59134i	0.605728	−	0.795672i	$-0.292882\pi$
$618$	3.28280	−	5.87220i	0.132054	−	0.236214i
$619$	−1.24836	−	1.71822i	−0.0501758	−	0.0690610i	0.783192	−	0.621780i	$-0.213590\pi$
$619$	−1.24836	−	1.71822i	−0.0501758	−	0.0690610i	−0.833368	+	0.552719i	$0.813590\pi$
$620$	3.54604	−	4.88070i	0.142412	−	0.196014i
$621$	28.9216	+	8.08651i	1.16058	+	0.324501i
$622$	17.0715	−	5.54685i	0.684503	−	0.222408i
$623$	9.66983	+	36.4606i	0.387413	+	1.46076i
$624$	8.20996	+	17.7737i	0.328661	+	0.711518i
$625$	4.02918	−	12.4006i	0.161167	−	0.496022i
$626$	8.52498			0.340727
$627$	0.819565	−	0.161186i	0.0327303	−	0.00643714i
$628$		−	2.46492i		−	0.0983612i
$629$	2.10239	−	6.47049i	0.0838277	−	0.257995i
$630$	−2.00798	+	4.19842i	−0.0799997	+	0.167269i
$631$	−2.52126	−	1.83180i	−0.100370	−	0.0729229i	0.536468	−	0.843920i	$-0.319758\pi$
$631$	−2.52126	−	1.83180i	−0.100370	−	0.0729229i	−0.636838	+	0.770997i	$0.719758\pi$
$632$	13.8508	−	4.50039i	0.550954	−	0.179016i
$633$	3.54873	+	29.7916i	0.141049	+	1.18411i
$634$	−8.65153	−	6.28571i	−0.343596	−	0.249637i
$635$	−11.4823	+	8.34238i	−0.455661	+	0.331057i
$636$	27.1690	+	15.1886i	1.07732	+	0.602267i
$637$	−44.9286	+	9.31023i	−1.78014	+	0.368885i
$638$	0.144681	−	0.595019i	0.00572799	−	0.0235570i
$639$	−6.86917	+	16.6543i	−0.271740	+	0.658833i
$640$	−9.83969	−	3.19711i	−0.388948	−	0.126377i
$641$	20.9623	+	28.8521i	0.827959	+	1.13959i	0.988299	+	0.152526i	$0.0487409\pi$
$641$	20.9623	+	28.8521i	0.827959	+	1.13959i	−0.160340	+	0.987062i	$0.551259\pi$
$642$	−7.22446	−	7.80362i	−0.285127	−	0.307984i
$643$	41.5502	−	13.5005i	1.63858	−	0.532407i	0.662360	−	0.749185i	$-0.269555\pi$
$643$	41.5502	−	13.5005i	1.63858	−	0.532407i	0.976221	+	0.216778i	$0.0695548\pi$
$644$	−22.7205	−	8.78824i	−0.895313	−	0.346305i
$645$	−4.09700	−	4.42545i	−0.161319	−	0.174252i
$646$	0.264045	−	0.191840i	0.0103887	−	0.00754784i
$647$	−10.6883	+	32.8951i	−0.420199	+	1.29324i	0.487318	+	0.873225i	$0.337975\pi$
$647$	−10.6883	+	32.8951i	−0.420199	+	1.29324i	−0.907517	+	0.420015i	$0.862025\pi$
$648$	−14.5415	+	14.6290i	−0.571243	+	0.574682i
$649$	−17.6182	+	1.33509i	−0.691576	+	0.0524068i
$650$	17.3714			0.681362
$651$	6.96348	+	17.5460i	0.272920	+	0.687683i
$652$	21.3880	−	15.5393i	0.837618	−	0.608565i
$653$	−7.58534	+	10.4403i	−0.296837	+	0.408561i	−0.931220	−	0.364458i	$-0.881254\pi$
$653$	−7.58534	+	10.4403i	−0.296837	+	0.408561i	0.634383	+	0.773019i	$0.281254\pi$
$654$	1.34296	−	0.159971i	0.0525137	−	0.00625535i
$655$	−2.58166	−	7.94553i	−0.100874	−	0.310457i
$656$	11.2220	+	8.15327i	0.438146	+	0.318332i
$657$	5.87535	+	24.3119i	0.229219	+	0.948497i
$658$	2.92085	+	4.52297i	0.113867	+	0.176324i
$659$			0.761612i			0.0296682i	0.999890	+	0.0148341i	$0.00472201\pi$
$659$			0.761612i			0.0296682i	−0.999890	+	0.0148341i	$0.995278\pi$
$660$	−6.16553	−	5.72405i	−0.239993	−	0.222808i
$661$		−	43.9258i		−	1.70851i	−0.519851	−	0.854257i	$-0.674012\pi$
$661$		−	43.9258i		−	1.70851i	0.519851	−	0.854257i	$-0.325988\pi$
$662$	3.07087	+	0.997786i	0.119353	+	0.0387800i
$663$	16.7542	+	36.2711i	0.650680	+	1.40865i
$664$	20.1560	−	27.7423i	0.782203	−	1.07661i
$665$	0.329818	+	0.127573i	0.0127898	+	0.00494707i
$666$	−3.68834	−	0.284712i	−0.142920	−	0.0110324i
$667$	−1.35344	−	0.983332i	−0.0524054	−	0.0380748i
$668$	−2.23534	+	1.62407i	−0.0864877	+	0.0628370i
$669$	−32.4998	−	18.1688i	−1.25652	−	0.702445i
$670$			3.46135i			0.133723i
$671$	−5.83415	+	9.45867i	−0.225225	+	0.365148i
$672$	20.0551	−	16.6186i	0.773643	−	0.641075i
$673$	4.83768	−	14.8888i	0.186479	−	0.573923i	−0.813492	−	0.581576i	$-0.802436\pi$
$673$	4.83768	−	14.8888i	0.186479	−	0.573923i	0.999971	+	0.00765336i	$0.00243616\pi$
$674$	−1.86262	−	2.56367i	−0.0717453	−	0.0987490i
$675$	−7.51819	−	20.2386i	−0.289375	−	0.778983i
$676$	−14.7519	−	45.4017i	−0.567381	−	1.74622i
$677$	−13.0245	−	40.0854i	−0.500574	−	1.54061i	−0.808087	−	0.589064i	$-0.799497\pi$
$677$	−13.0245	−	40.0854i	−0.500574	−	1.54061i	0.307513	−	0.951544i	$-0.400503\pi$
$678$	8.55011	+	9.23555i	0.328365	+	0.354689i
$679$	2.03462	−	37.0137i	0.0780817	−	1.42046i
$680$	−7.05132	−	2.29111i	−0.270406	−	0.0878602i
$681$	−27.5804	−	5.46457i	−1.05688	−	0.209403i
$682$	8.68950	−	0.658480i	0.332738	−	0.0252145i
$683$		−	48.6985i		−	1.86339i	−0.363236	−	0.931697i	$-0.618328\pi$
$683$		−	48.6985i		−	1.86339i	0.363236	−	0.931697i	$-0.381672\pi$
$684$	0.529114	+	0.450535i	0.0202312	+	0.0172266i
$685$	5.40403	+	7.43801i	0.206478	+	0.284192i
$686$	5.28216	+	10.5662i	0.201674	+	0.403420i
$687$	−44.0393	+	5.24589i	−1.68020	+	0.200143i
$688$	2.01845	+	6.21215i	0.0769526	+	0.236836i
$689$	−59.8163	−	43.4591i	−2.27882	−	1.65566i
$690$	5.32838	−	2.46127i	0.202848	−	0.0936988i
$691$	6.04359	+	1.96368i	0.229909	+	0.0747020i	0.421706	−	0.906733i	$-0.361431\pi$
$691$	6.04359	+	1.96368i	0.229909	+	0.0747020i	−0.191797	+	0.981435i	$0.561431\pi$
$692$	−18.0948			−0.687863
$693$	25.4547	−	6.71264i	0.966943	−	0.254992i
$694$	−8.41079			−0.319269
$695$	2.14144	+	0.695797i	0.0812295	+	0.0263931i
$696$	1.04316	−	0.481851i	0.0395407	−	0.0182645i
$697$	22.9010	+	16.6385i	0.867437	+	0.630230i
$698$	−1.15870	−	3.56612i	−0.0438576	−	0.134980i
$699$	28.2832	−	3.36905i	1.06977	−	0.127429i
$700$	4.48965	+	16.9284i	0.169693	+	0.639835i
$701$	8.80924	+	12.1249i	0.332720	+	0.457950i	0.942298	−	0.334776i	$-0.108661\pi$
$701$	8.80924	+	12.1249i	0.332720	+	0.457950i	−0.609577	+	0.792727i	$0.708661\pi$
$702$	17.0302	−	13.4878i	0.642765	−	0.509064i
$703$			0.281097i			0.0106018i
$704$	−0.222193	−	0.540862i	−0.00837422	−	0.0203845i
$705$	4.98295	+	0.987286i	0.187669	+	0.0371833i
$706$	20.0123	+	6.50239i	0.753173	+	0.244721i
$707$	−33.9596	−	1.86674i	−1.27718	−	0.0702059i
$708$	−9.98675	−	10.7874i	−0.375325	−	0.405414i
$709$	−9.00152	−	27.7038i	−0.338059	−	1.04044i	−0.965195	−	0.261530i	$-0.915773\pi$
$709$	−9.00152	−	27.7038i	−0.338059	−	1.04044i	0.627136	−	0.778909i	$-0.284227\pi$
$710$	1.08805	+	3.34867i	0.0408337	+	0.125673i
$711$	9.98498	+	16.2393i	0.374466	+	0.609020i
$712$	19.2062	+	26.4351i	0.719783	+	0.990696i
$713$	7.35695	−	22.6424i	0.275520	−	0.847964i
$714$	7.92046	−	6.56324i	0.296416	−	0.245623i
$715$	12.9344	+	15.2337i	0.483721	+	0.569708i
$716$			28.2603i			1.05614i
$717$	−16.2350	−	9.07603i	−0.606306	−	0.338951i
$718$	−5.39810	+	3.92195i	−0.201455	+	0.146366i
$719$	9.56768	+	6.95132i	0.356814	+	0.259241i	0.751722	−	0.659480i	$-0.229224\pi$
$719$	9.56768	+	6.95132i	0.356814	+	0.259241i	−0.394908	+	0.918721i	$0.629224\pi$
$720$	0.366015	−	4.74159i	0.0136406	−	0.176709i
$721$	−15.0264	−	5.81219i	−0.559614	−	0.216457i
$722$	7.11541	−	9.79353i	0.264808	−	0.364477i
$723$	13.1811	+	28.5357i	0.490211	+	1.06126i
$724$	14.3078	+	4.64887i	0.531744	+	0.172774i
$725$			1.20272i			0.0446680i
$726$	0.538555	−	12.1405i	0.0199876	−	0.450578i
$727$			12.4488i			0.461701i	0.972989	+	0.230850i	$0.0741508\pi$
$727$			12.4488i			0.461701i	−0.972989	+	0.230850i	$0.925849\pi$
$728$	−33.3889	+	21.5619i	−1.23747	+	0.799138i
$729$	−23.0845	−	14.0037i	−0.854983	−	0.518656i
$730$	3.95481	+	2.87334i	0.146374	+	0.106347i
$731$	4.11909	+	12.6772i	0.152350	+	0.468885i
$732$	−9.18130	+	1.09366i	−0.339351	+	0.0404229i
$733$	24.2405	−	33.3642i	0.895344	−	1.23234i	−0.0765850	−	0.997063i	$-0.524402\pi$
$733$	24.2405	−	33.3642i	0.895344	−	1.23234i	0.971929	−	0.235273i	$-0.0755983\pi$
$734$	3.11968	−	2.26658i	0.115149	−	0.0836609i
$735$	10.6295	+	3.35141i	0.392075	+	0.123619i
$736$	−32.8483			−1.21081
$737$	14.9250	−	12.6724i	0.549771	−	0.466793i
$738$	5.86882	−	14.2289i	0.216034	−	0.523774i
$739$	4.14775	−	12.7655i	0.152578	−	0.469586i	−0.845330	−	0.534245i	$-0.820596\pi$
$739$	4.14775	−	12.7655i	0.152578	−	0.469586i	0.997907	+	0.0646592i	$0.0205960\pi$
$740$	2.29055	−	1.66418i	0.0842024	−	0.0611766i
$741$	−1.12144	−	1.21135i	−0.0411972	−	0.0444999i
$742$	−6.86713	+	17.7538i	−0.252100	+	0.651763i
$743$	33.2762	−	10.8121i	1.22079	−	0.396657i	0.373417	−	0.927663i	$-0.378186\pi$
$743$	33.2762	−	10.8121i	1.22079	−	0.396657i	0.847368	+	0.531006i	$0.178186\pi$
$744$	11.1090	+	11.9995i	0.407275	+	0.439925i
$745$	−5.71521	−	7.86631i	−0.209389	−	0.288199i
$746$	3.67058	+	1.19264i	0.134389	+	0.0436657i
$747$	41.4956	+	17.1152i	1.51825	+	0.626211i
$748$	7.06608	+	17.2002i	0.258361	+	0.628902i
$749$	−16.0778	+	19.7510i	−0.587469	+	0.721687i
$750$	−8.11539	−	4.53684i	−0.296332	−	0.165662i
$751$	−15.1867	+	11.0338i	−0.554170	+	0.402628i	−0.829320	−	0.558773i	$-0.811272\pi$
$751$	−15.1867	+	11.0338i	−0.554170	+	0.402628i	0.275151	+	0.961401i	$0.411272\pi$
$752$	−4.45112	−	3.23393i	−0.162316	−	0.117929i
$753$	1.77288	+	14.8833i	0.0646073	+	0.542379i
$754$	−1.15098	+	0.373977i	−0.0419163	+	0.0136194i
$755$	11.4625	+	8.32801i	0.417164	+	0.303087i
$756$	17.5453	+	13.1100i	0.638118	+	0.476808i
$757$	−4.27923	+	13.1701i	−0.155531	+	0.478676i	−0.998214	−	0.0597337i	$-0.980975\pi$
$757$	−4.27923	+	13.1701i	−0.155531	+	0.478676i	0.842683	+	0.538410i	$0.180975\pi$
$758$			2.85199i			0.103589i
$759$	−30.1206	−	13.9646i	−1.09331	−	0.506882i
$760$	0.306330			0.0111118
$761$	−9.15398	+	28.1730i	−0.331831	+	1.02127i	0.636431	+	0.771334i	$0.280410\pi$
$761$	−9.15398	+	28.1730i	−0.331831	+	1.02127i	−0.968262	+	0.249938i	$0.919590\pi$
$762$	−7.15281	−	15.4851i	−0.259119	−	0.560965i
$763$	−0.830296	−	3.13067i	−0.0300587	−	0.113338i
$764$	−2.46882	+	0.802169i	−0.0893189	+	0.0290215i
$765$	0.746933	−	9.67626i	0.0270054	−	0.349846i
$766$	6.71471	−	9.24200i	0.242612	−	0.333927i
$767$	20.5250	+	28.2502i	0.741114	+	1.02006i
$768$	6.36542	−	11.3863i	0.229692	−	0.410868i
$769$			16.3295i			0.588856i	0.955674	+	0.294428i	$0.0951291\pi$
$769$			16.3295i			0.588856i	−0.955674	+	0.294428i	$0.904871\pi$
$770$	2.93731	−	4.22421i	0.105853	−	0.152230i
$771$	−11.3410	−	2.24703i	−0.408438	−	0.0809249i
$772$	5.42179	−	16.6866i	0.195135	−	0.600562i
$773$	0.756196	−	0.549409i	0.0271985	−	0.0197609i	−0.574103	−	0.818783i	$-0.694649\pi$
$773$	0.756196	−	0.549409i	0.0271985	−	0.0197609i	0.601301	+	0.799022i	$0.294649\pi$
$774$	6.17412	−	3.79626i	0.221924	−	0.136454i
$775$	−16.2782	+	5.28910i	−0.584729	+	0.189990i
$776$	−9.92292	−	30.5396i	−0.356212	−	1.09631i
$777$	0.563474	+	8.84134i	0.0202145	+	0.317181i
$778$	−10.7748	+	7.82836i	−0.386296	+	0.280660i
$779$	−1.11232	−	0.361413i	−0.0398529	−	0.0129490i
$780$	−3.23150	+	16.3098i	−0.115706	+	0.583983i
$781$	10.4557	−	16.9514i	0.374135	−	0.606570i
$782$	−12.9729			−0.463911
$783$	0.933839	+	1.17910i	0.0333727	+	0.0421377i
$784$	−8.92940	−	8.12305i	−0.318907	−	0.290109i
$785$	0.835982	−	1.15063i	0.0298375	−	0.0410678i
$786$	9.96999	−	1.18761i	0.355618	−	0.0423606i
$787$	−33.5176	+	10.8905i	−1.19477	+	0.388205i	−0.837835	−	0.545924i	$-0.816179\pi$
$787$	−33.5176	+	10.8905i	−1.19477	+	0.388205i	−0.356937	+	0.934128i	$0.616179\pi$
$788$	0.569136	−	0.783348i	0.0202746	−	0.0279056i
$789$	−9.86954	−	21.3665i	−0.351365	−	0.760668i
$790$	3.54349	+	1.15135i	0.126072	+	0.0409632i
$791$	19.0280	−	23.3752i	0.676557	−	0.831128i
$792$	18.4674	−	13.3777i	0.656211	−	0.475358i
$793$	21.9633			0.779941
$794$	5.55118	−	17.0848i	0.197004	−	0.606315i
$795$	7.53129	+	16.3044i	0.267107	+	0.578259i
$796$	5.62169	−	7.73759i	0.199255	−	0.274252i
$797$	5.14081	+	15.8218i	0.182097	+	0.560437i	0.999886	−	0.0150809i	$-0.00480058\pi$
$797$	5.14081	+	15.8218i	0.182097	+	0.560437i	−0.817789	+	0.575518i	$0.804801\pi$
$798$	−0.227434	+	0.359024i	−0.00805107	+	0.0127093i
$799$	−9.08349	−	6.59954i	−0.321351	−	0.233475i
$800$	13.8808	+	19.1053i	0.490762	+	0.675475i
$801$	−27.7291	+	32.5655i	−0.979761	+	1.15064i
$802$	15.2208			0.537465
$803$	−2.08941	−	27.5725i	−0.0737336	−	0.973011i
$804$	15.9793	+	3.16602i	0.563547	+	0.111657i
$805$	−7.62543	−	11.8081i	−0.268761	−	0.416179i
$806$	−10.1231	−	13.9333i	−0.356572	−	0.490780i
$807$	23.0237	+	24.8695i	0.810473	+	0.875446i
$808$	−28.0197	+	9.10414i	−0.985728	+	0.320282i
$809$	27.5339	−	8.94629i	0.968039	−	0.314535i	0.218015	−	0.975945i	$-0.430042\pi$
$809$	27.5339	−	8.94629i	0.968039	−	0.314535i	0.750024	+	0.661411i	$0.230042\pi$
$810$	−5.20955	+	0.841141i	−0.183045	+	0.0295547i
$811$	−0.995512	−	1.37020i	−0.0349571	−	0.0481144i	0.791181	−	0.611583i	$-0.209467\pi$
$811$	−0.995512	−	1.37020i	−0.0349571	−	0.0481144i	−0.826138	+	0.563468i	$0.809467\pi$
$812$	−0.661913	−	1.02498i	−0.0232286	−	0.0359697i
$813$	−2.82347	+	14.2504i	−0.0990235	+	0.499784i
$814$	3.97396	+	0.966283i	0.139287	+	0.0338682i
$815$	15.2541			0.534328
$816$	−5.12922	+	9.17502i	−0.179559	+	0.321190i
$817$	−0.323715	−	0.445555i	−0.0113253	−	0.0155880i
$818$	15.3612	+	11.1606i	0.537093	+	0.390221i
$819$	−37.7009	−	35.8525i	−1.31738	−	1.25279i
$820$	3.64025	+	11.2035i	0.127123	+	0.391244i
$821$	−21.7540	+	29.9418i	−0.759219	+	1.04498i	0.238059	+	0.971251i	$0.423489\pi$
$821$	−21.7540	+	29.9418i	−0.759219	+	1.04498i	−0.997279	+	0.0737249i	$0.976511\pi$
$822$	−10.0309	+	4.63345i	−0.349869	+	0.161610i
$823$	−3.67052	+	11.2967i	−0.127946	+	0.393778i	−0.994426	−	0.105434i	$-0.966377\pi$
$823$	−3.67052	+	11.2967i	−0.127946	+	0.393778i	0.866480	+	0.499212i	$0.166377\pi$
$824$	−13.9563			−0.486191
$825$	4.60605	+	23.4199i	0.160362	+	0.815376i
$826$	5.67555	−	6.97223i	0.197478	−	0.242595i
$827$	1.56101	+	0.507203i	0.0542816	+	0.0176372i	0.336032	−	0.941851i	$-0.390915\pi$
$827$	1.56101	+	0.507203i	0.0542816	+	0.0176372i	−0.281750	+	0.959488i	$0.590915\pi$
$828$	−6.48868	−	26.8498i	−0.225497	−	0.933094i
$829$	15.3748	−	21.1615i	0.533988	−	0.734971i	−0.453744	−	0.891132i	$-0.649912\pi$
$829$	15.3748	−	21.1615i	0.533988	−	0.734971i	0.987732	+	0.156161i	$0.0499119\pi$
$830$	8.34351	−	2.71097i	0.289607	−	0.0940992i
$831$	−2.02822	−	17.0269i	−0.0703581	−	0.590657i
$832$	−0.679246	+	0.934902i	−0.0235486	+	0.0324119i
$833$	−18.2224	−	16.5769i	−0.631368	−	0.574354i
$834$	−1.32047	+	2.36202i	−0.0457241	+	0.0817901i
$835$	−1.59426			−0.0551717
$836$	−0.497262	−	0.585657i	−0.0171982	−	0.0202554i
$837$	−11.8518	+	17.8242i	−0.409659	+	0.616095i
$838$	11.0190	+	3.58029i	0.380645	+	0.123679i
$839$	43.7807	−	31.8085i	1.51148	−	1.09815i	0.545960	−	0.837811i	$-0.316165\pi$
$839$	43.7807	−	31.8085i	1.51148	−	1.09815i	0.965517	−	0.260341i	$-0.0838349\pi$
$840$	9.63500	−	0.614055i	0.332439	−	0.0211869i
$841$	8.93560	+	27.5009i	0.308124	+	0.948309i
$842$	−4.58937	+	1.49118i	−0.158160	+	0.0513893i
$843$	−25.9811	+	24.0528i	−0.894836	+	0.828424i
$844$	22.3260	−	16.2208i	0.768491	−	0.558341i
$845$	8.51183	−	26.1967i	0.292816	−	0.901194i
$846$	−2.32782	+	5.64379i	−0.0800321	+	0.194037i
$847$	−28.9683	+	2.79989i	−0.995362	+	0.0962053i
$848$		−	19.4521i		−	0.667987i
$849$	29.4158	+	16.4447i	1.00955	+	0.564380i
$850$	5.48202	+	7.54535i	0.188032	+	0.258803i
$851$	6.56739	−	9.03923i	0.225127	−	0.309861i
$852$	16.4543	−	1.96002i	0.563716	−	0.0671490i
$853$	−9.81437	+	3.18888i	−0.336038	+	0.109185i	−0.472175	−	0.881505i	$-0.656531\pi$
$853$	−9.81437	+	3.18888i	−0.336038	+	0.109185i	0.136138	+	0.990690i	$0.456531\pi$
$854$	−1.44957	−	5.46567i	−0.0496033	−	0.187031i
$855$	0.0941917	+	0.389760i	0.00322129	+	0.0133295i
$856$	−6.81725	+	20.9813i	−0.233009	+	0.717127i
$857$	21.1871			0.723738			0.361869	−	0.932229i	$-0.382139\pi$
$857$	21.1871			0.723738			0.361869	+	0.932229i	$0.382139\pi$
$858$	−20.9802	+	11.6901i	−0.716252	+	0.399095i
$859$			42.4009i			1.44670i	0.690482	+	0.723350i	$0.257399\pi$
$859$			42.4009i			1.44670i	−0.690482	+	0.723350i	$0.742601\pi$
$860$	−1.71417	+	5.27566i	−0.0584526	+	0.179899i
$861$	−35.7102	−	9.13784i	−1.21700	−	0.311417i
$862$	2.63610	+	1.91524i	0.0897859	+	0.0652333i
$863$	−47.6123	+	15.4702i	−1.62074	+	0.526611i	−0.972116	−	0.234499i	$-0.924655\pi$
$863$	−47.6123	+	15.4702i	−1.62074	+	0.526611i	−0.648624	+	0.761109i	$0.724655\pi$
$864$	28.4423	+	7.95252i	0.967628	+	0.270550i
$865$	−8.44670	−	6.13689i	−0.287197	−	0.208661i
$866$	−9.28394	+	6.74518i	−0.315481	+	0.229211i
$867$	3.90082	−	6.97768i	0.132479	−	0.236975i
$868$	10.9617	−	13.4661i	0.372064	−	0.457068i
$869$	−8.00859	−	19.4945i	−0.271673	−	0.661305i
$870$	0.288364	+	0.0571344i	0.00977647	+	0.00193704i
$871$	−36.8010	−	11.9574i	−1.24696	−	0.405160i
$872$	−1.64913	−	2.26984i	−0.0558467	−	0.0768664i
$873$	35.8060	−	22.0159i	1.21185	−	0.745126i
$874$	0.509765	−	0.165633i	0.0172431	−	0.00560261i
$875$	−8.03246	+	20.7666i	−0.271547	+	0.702038i
$876$	16.8822	−	15.6292i	0.570396	−	0.528062i
$877$	−9.12186	+	6.62742i	−0.308023	+	0.223792i	−0.731048	−	0.682326i	$-0.760968\pi$
$877$	−9.12186	+	6.62742i	−0.308023	+	0.223792i	0.423025	+	0.906118i	$0.360968\pi$
$878$	−4.09138	+	12.5920i	−0.138078	+	0.424959i
$879$	−22.7832	−	4.51409i	−0.768457	−	0.152256i
$880$	−1.24222	+	5.10877i	−0.0418751	+	0.172216i
$881$	−7.27220			−0.245007			−0.122503	−	0.992468i	$-0.539092\pi$
$881$	−7.27220			−0.245007			−0.122503	+	0.992468i	$0.539092\pi$
$882$	−6.43380	+	11.7483i	−0.216637	+	0.395586i
$883$	33.6795	−	24.4696i	1.13340	−	0.823467i	0.147218	−	0.989104i	$-0.452968\pi$
$883$	33.6795	−	24.4696i	1.13340	−	0.823467i	0.986187	+	0.165637i	$0.0529681\pi$
$884$	21.6010	−	29.7313i	0.726522	−	0.999971i
$885$	−1.00328	−	8.42258i	−0.0337250	−	0.283122i
$886$	−4.95686	−	15.2557i	−0.166529	−	0.512524i
$887$	41.7380	+	30.3244i	1.40142	+	1.01819i	0.994500	+	0.104732i	$0.0333985\pi$
$887$	41.7380	+	30.3244i	1.40142	+	1.01819i	0.406924	+	0.913462i	$0.366602\pi$
$888$	3.21814	+	6.96693i	0.107994	+	0.233795i
$889$	−34.3159	+	22.1606i	−1.15092	+	0.743244i
$890$			8.35951i			0.280211i
$891$	22.6997	+	19.3836i	0.760468	+	0.649376i
$892$			34.2479i			1.14670i
$893$	0.441191	+	0.143352i	0.0147639	+	0.00479708i
$894$	10.6085	−	4.90025i	0.354802	−	0.163889i
$895$	−9.58453	+	13.1920i	−0.320375	+	0.440959i
$896$	−27.7724	−	10.7423i	−0.927812	−	0.358875i
$897$	7.76104	+	65.1540i	0.259134	+	2.17543i
$898$	−0.459217	−	0.333641i	−0.0153243	−	0.0111337i
$899$	0.964683	−	0.700884i	0.0321740	−	0.0233758i
$900$	−12.8745	+	15.1200i	−0.429149	+	0.503999i
$901$		−	39.6962i		−	1.32247i
$902$	−8.93306	+	14.4828i	−0.297438	+	0.482224i
$903$	−11.0749	−	13.3651i	−0.368551	−	0.444764i
$904$	8.06818	−	24.8313i	0.268344	−	0.825877i
$905$	5.10222	+	7.02260i	0.169603	+	0.233439i
$906$	−12.4953	+	11.5679i	−0.415128	+	0.384318i
$907$	10.7685	+	33.1421i	0.357563	+	1.10046i	0.954509	+	0.298183i	$0.0963806\pi$
$907$	10.7685	+	33.1421i	0.357563	+	1.10046i	−0.596946	+	0.802281i	$0.703619\pi$
$908$	7.99176	+	24.5961i	0.265216	+	0.816251i
$909$	−20.1993	−	32.8515i	−0.669968	−	1.08962i
$910$	−10.1530	−	0.558104i	−0.336569	−	0.0185010i
$911$	3.65800	+	1.18856i	0.121195	+	0.0393786i	0.368987	−	0.929435i	$-0.379705\pi$
$911$	3.65800	+	1.18856i	0.121195	+	0.0393786i	−0.247792	+	0.968813i	$0.579705\pi$
$912$	0.0844076	−	0.426015i	0.00279501	−	0.0141068i
$913$	−42.2360	−	26.0514i	−1.39781	−	0.862175i
$914$			11.2920i			0.373505i
$915$	−4.65677	−	2.60333i	−0.153948	−	0.0860633i
$916$	23.9782	+	33.0032i	0.792263	+	1.09046i
$917$	−6.16405	−	23.2418i	−0.203555	−	0.767513i
$918$	11.2329	+	3.14072i	0.370739	+	0.103659i
$919$	5.63075	+	17.3297i	0.185741	+	0.571653i	0.999960	−	0.00890468i	$-0.00283449\pi$
$919$	5.63075	+	17.3297i	0.185741	+	0.571653i	−0.814219	+	0.580558i	$0.802834\pi$
$920$	−9.85066	−	7.15692i	−0.324767	−	0.235957i
$921$	−16.7260	−	36.2101i	−0.551141	−	1.19316i
$922$	4.75119	+	1.54375i	0.156472	+	0.0508408i
$923$	−39.3617			−1.29561
$924$	−16.8144	−	17.4239i	−0.553153	−	0.573204i
$925$	−8.03262			−0.264111
$926$	1.70564	+	0.554197i	0.0560509	+	0.0182120i
$927$	−4.29135	−	17.7574i	−0.140946	−	0.583228i
$928$	−1.33101	−	0.967038i	−0.0436927	−	0.0317446i
$929$	8.36150	+	25.7341i	0.274332	+	0.844307i	0.989395	+	0.145248i	$0.0463979\pi$
$929$	8.36150	+	25.7341i	0.274332	+	0.844307i	−0.715063	+	0.699060i	$0.753602\pi$
$930$	0.494831	+	4.15411i	0.0162261	+	0.136218i
$931$	0.927686	+	0.418724i	0.0304037	+	0.0137231i
$932$	−15.3994	−	21.1955i	−0.504426	−	0.694282i
$933$	23.7850	−	42.5460i	0.778686	−	1.39289i
$934$		−	5.77920i		−	0.189101i
$935$	−2.53501	+	10.4256i	−0.0829038	+	0.340952i
$936$	−41.6628	−	17.1841i	−1.36179	−	0.561681i
$937$	−5.07987	−	1.65055i	−0.165952	−	0.0539212i	0.224863	−	0.974391i	$-0.427807\pi$
$937$	−5.07987	−	1.65055i	−0.165952	−	0.0539212i	−0.390815	+	0.920469i	$0.627807\pi$
$938$	−0.546797	+	9.94729i	−0.0178535	+	0.324790i
$939$	16.9874	−	15.7267i	0.554364	−	0.513220i
$940$	−1.44387	−	4.44379i	−0.0470940	−	0.144940i
$941$	16.0310	+	49.3384i	0.522597	+	1.60839i	0.769020	+	0.639225i	$0.220745\pi$
$941$	16.0310	+	49.3384i	0.522597	+	1.60839i	−0.246423	+	0.969162i	$0.579255\pi$
$942$	1.16121	+	1.25430i	0.0378342	+	0.0408673i
$943$	27.3249	+	37.6095i	0.889821	+	1.22473i
$944$	−2.83890	+	8.73725i	−0.0923984	+	0.284373i
$945$	3.74391	+	12.0703i	0.121789	+	0.392647i
$946$	−7.41174	+	3.04484i	−0.240977	+	0.0989964i
$947$		−	3.70206i		−	0.120301i	−0.998189	−	0.0601504i	$-0.980842\pi$
$947$		−	3.70206i		−	0.120301i	0.998189	−	0.0601504i	$-0.0191580\pi$
$948$	8.55637	−	15.3054i	0.277898	−	0.497097i
$949$	−44.2115	+	32.1215i	−1.43516	+	1.04271i
$950$	−0.311749	−	0.226499i	−0.0101145	−	0.00734859i
$951$	−28.8353	+	3.43482i	−0.935050	+	0.111382i
$952$	−19.9023	−	7.69816i	−0.645037	−	0.249499i
$953$	−35.7696	+	49.2327i	−1.15869	+	1.59480i	−0.442744	+	0.896648i	$0.645995\pi$
$953$	−35.7696	+	49.2327i	−1.15869	+	1.59480i	−0.715947	+	0.698154i	$0.754005\pi$
$954$	−20.9804	+	5.07026i	−0.679266	+	0.164156i
$955$	−1.42451	−	0.462851i	−0.0460960	−	0.0149775i
$956$			17.1082i			0.553319i
$957$	−0.809376	−	1.45258i	−0.0261634	−	0.0469552i
$958$			1.29019i			0.0416841i
$959$	14.3552	+	22.2292i	0.463554	+	0.717818i
$960$	0.254831	−	0.117711i	0.00822465	−	0.00379910i
$961$	−11.3512	−	8.24710i	−0.366166	−	0.266036i
$962$	−2.49768	−	7.68707i	−0.0805285	−	0.247841i
$963$	−28.7919	−	2.22251i	−0.927805	−	0.0716195i
$964$	16.9943	−	23.3906i	0.547349	−	0.753361i
$965$	8.19017	−	5.95051i	0.263651	−	0.191554i
$966$	15.7016	−	6.23150i	0.505192	−	0.200495i
$967$	0.0489497			0.00157412			0.000787058	−	1.00000i	$-0.499749\pi$
$967$	0.0489497			0.00157412			0.000787058		1.00000i	$0.499749\pi$
$968$	−22.5288	+	11.3146i	−0.724104	+	0.363664i
$969$	0.172252	−	0.869377i	0.00553353	−	0.0279284i
$970$	2.53862	−	7.81306i	0.0815101	−	0.250862i
$971$	−13.3361	+	9.68927i	−0.427977	+	0.310943i	−0.780839	−	0.624732i	$-0.785208\pi$
$971$	−13.3361	+	9.68927i	−0.427977	+	0.310943i	0.352863	+	0.935675i	$0.385208\pi$
$972$	−0.881937	+	24.8193i	−0.0282881	+	0.796078i
$973$	6.04420	+	2.33788i	0.193768	+	0.0749491i
$974$	14.3151	−	4.65125i	0.458685	−	0.149036i
$975$	34.6154	−	32.0463i	1.10858	−	1.02630i
$976$	3.39642	+	4.67477i	0.108717	+	0.149636i
$977$	23.1164	+	7.51097i	0.739559	+	0.240297i	0.654482	−	0.756077i	$-0.272887\pi$
$977$	23.1164	+	7.51097i	0.739559	+	0.240297i	0.0850764	+	0.996374i	$0.472887\pi$
$978$	−3.56303	+	17.9830i	−0.113933	+	0.575034i
$979$	36.0455	−	30.6051i	1.15202	−	0.978143i
$980$	−2.08017	−	10.0383i	−0.0664487	−	0.320663i
$981$	2.38095	−	2.79622i	0.0760180	−	0.0892764i
$982$	1.95107	−	1.41753i	0.0622610	−	0.0452353i
$983$	13.6836	+	9.94169i	0.436438	+	0.317091i	0.784218	−	0.620485i	$-0.213064\pi$
$983$	13.6836	+	9.94169i	0.436438	+	0.317091i	−0.347780	+	0.937576i	$0.613064\pi$
$984$	−31.7062	+	3.77679i	−1.01076	+	0.120400i
$985$	0.531347	−	0.172645i	0.0169301	−	0.00550093i
$986$	−0.525663	−	0.381917i	−0.0167405	−	0.0121627i
$987$	14.1641	+	3.62445i	0.450850	+	0.115368i
$988$	−0.469206	+	1.44407i	−0.0149274	+	0.0459419i
$989$			21.8908i			0.696087i
$990$	5.83395	+	0.00819899i	0.185415	+	0.000260581i
$991$	13.3982			0.425608			0.212804	−	0.977095i	$-0.431740\pi$
$991$	13.3982			0.425608			0.212804	+	0.977095i	$0.431740\pi$
$992$	7.23505	−	22.2672i	0.229713	−	0.706984i
$993$	7.95991	−	3.67681i	0.252600	−	0.116680i
$994$	2.59786	+	9.79535i	0.0823990	+	0.310689i
$995$	5.24843	−	1.70532i	0.166386	−	0.0540622i
$996$	−4.88356	−	40.9975i	−0.154742	−	1.29906i
$997$	−16.1879	+	22.2807i	−0.512674	+	0.705636i	−0.984367	−	0.176127i	$-0.943643\pi$
$997$	−16.1879	+	22.2807i	−0.512674	+	0.705636i	0.471693	+	0.881763i	$0.343643\pi$
$998$	−5.68253	−	7.82134i	−0.179877	−	0.247580i
$999$	−7.87487	+	6.23683i	−0.249150	+	0.197325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.u.a.20.18	yes	112
3.2	odd	2	inner	231.2.u.a.20.11	✓	112
7.6	odd	2	inner	231.2.u.a.20.17	yes	112
11.5	even	5	inner	231.2.u.a.104.12	yes	112
21.20	even	2	inner	231.2.u.a.20.12	yes	112
33.5	odd	10	inner	231.2.u.a.104.17	yes	112
77.27	odd	10	inner	231.2.u.a.104.11	yes	112
231.104	even	10	inner	231.2.u.a.104.18	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.u.a.20.11	✓	112	3.2	odd	2	inner
231.2.u.a.20.12	yes	112	21.20	even	2	inner
231.2.u.a.20.17	yes	112	7.6	odd	2	inner
231.2.u.a.20.18	yes	112	1.1	even	1	trivial
231.2.u.a.104.11	yes	112	77.27	odd	10	inner
231.2.u.a.104.12	yes	112	11.5	even	5	inner
231.2.u.a.104.17	yes	112	33.5	odd	10	inner
231.2.u.a.104.18	yes	112	231.104	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.u (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.606621 + 0.197103i) q^{2} +(1.57241 - 0.726320i) q^{3} +(-1.28889 - 0.936436i) q^{4} +(-0.284064 - 0.874260i) q^{5} +(1.09702 - 0.130675i) q^{6} +(-0.678241 - 2.55734i) q^{7} +(-1.34712 - 1.85415i) q^{8} +(1.94492 - 2.28414i) q^{9} +O(q^{10})\)	\(q+(0.606621 + 0.197103i) q^{2} +(1.57241 - 0.726320i) q^{3} +(-1.28889 - 0.936436i) q^{4} +(-0.284064 - 0.874260i) q^{5} +(1.09702 - 0.130675i) q^{6} +(-0.678241 - 2.55734i) q^{7} +(-1.34712 - 1.85415i) q^{8} +(1.94492 - 2.28414i) q^{9} -0.586335i q^{10} +(-2.52823 + 2.14664i) q^{11} +(-2.70682 - 0.536309i) q^{12} +(6.23392 + 2.02552i) q^{13} +(0.0926247 - 1.68502i) q^{14} +(-1.08166 - 1.16837i) q^{15} +(0.532894 + 1.64008i) q^{16} +(1.08749 + 3.34694i) q^{17} +(1.63004 - 1.00226i) q^{18} +(-0.0854645 - 0.117632i) q^{19} +(-0.452560 + 1.39284i) q^{20} +(-2.92392 - 3.52856i) q^{21} +(-1.95679 + 0.803875i) q^{22} +5.77943i q^{23} +(-3.46493 - 1.93704i) q^{24} +(3.36145 - 2.44223i) q^{25} +(3.38239 + 2.45745i) q^{26} +(1.39919 - 5.00423i) q^{27} +(-1.52061 + 3.93127i) q^{28} +(-0.170143 + 0.234182i) q^{29} +(-0.425867 - 0.921956i) q^{30} +(-3.91775 - 1.27295i) q^{31} +5.68366i q^{32} +(-2.41626 + 5.21169i) q^{33} +2.24467i q^{34} +(-2.04312 + 1.31941i) q^{35} +(-4.64575 + 1.12272i) q^{36} +(-1.56403 - 1.13634i) q^{37} +(-0.0286590 - 0.0882033i) q^{38} +(11.2734 - 1.34287i) q^{39} +(-1.23834 + 1.70443i) q^{40} +(6.50747 - 4.72795i) q^{41} +(-1.07822 - 2.71681i) q^{42} +3.78771 q^{43} +(5.26881 - 0.399264i) q^{44} +(-2.54941 - 1.05152i) q^{45} +(-1.13914 + 3.50593i) q^{46} +(-2.58114 + 1.87530i) q^{47} +(2.02915 + 2.19182i) q^{48} +(-6.07998 + 3.46899i) q^{49} +(2.52050 - 0.818960i) q^{50} +(4.14092 + 4.47289i) q^{51} +(-6.13808 - 8.44835i) q^{52} +(-10.7279 - 3.48570i) q^{53} +(1.83513 - 2.75989i) q^{54} +(2.59490 + 1.60055i) q^{55} +(-3.82803 + 4.70261i) q^{56} +(-0.219823 - 0.122890i) q^{57} +(-0.149371 + 0.108524i) q^{58} +(4.30990 + 3.13133i) q^{59} +(0.300037 + 2.51881i) q^{60} +(3.18676 - 1.03544i) q^{61} +(-2.12569 - 1.54440i) q^{62} +(-7.16044 - 3.42463i) q^{63} +(-0.0544799 + 0.167672i) q^{64} -6.02544i q^{65} +(-2.49299 + 2.68527i) q^{66} -5.90336 q^{67} +(1.73254 - 5.33222i) q^{68} +(4.19771 + 9.08761i) q^{69} +(-1.49946 + 0.397676i) q^{70} +(-5.71118 + 1.85568i) q^{71} +(-6.85519 - 0.529168i) q^{72} +(-4.90051 + 6.74497i) q^{73} +(-0.724801 - 0.997603i) q^{74} +(3.51172 - 6.28167i) q^{75} +0.231647i q^{76} +(7.20443 + 5.00960i) q^{77} +(7.10338 + 1.40741i) q^{78} +(-1.96364 + 6.04346i) q^{79} +(1.28248 - 0.931776i) q^{80} +(-1.43457 - 8.88493i) q^{81} +(4.87947 - 1.58544i) q^{82} +(4.62359 + 14.2299i) q^{83} +(0.464349 + 7.28600i) q^{84} +(2.61718 - 1.90149i) q^{85} +(2.29771 + 0.746570i) q^{86} +(-0.0974433 + 0.491808i) q^{87} +(7.38603 + 1.79594i) q^{88} -14.2572 q^{89} +(-1.33927 - 1.14037i) q^{90} +(0.951853 - 17.3160i) q^{91} +(5.41207 - 7.44907i) q^{92} +(-7.08487 + 0.843939i) q^{93} +(-1.93540 + 0.628850i) q^{94} +(-0.0785634 + 0.108133i) q^{95} +(4.12816 + 8.93702i) q^{96} +(13.3252 + 4.32964i) q^{97} +(-4.37199 + 0.905977i) q^{98} +(-0.0139835 + 9.94986i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9}+O(q^{10}) \) 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9	\( 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9} - 60 q^{16} + 2 q^{18} - 80 q^{22} - 36 q^{25} + 8 q^{28} + 24 q^{30} - 34 q^{36} + 4 q^{37} - 66 q^{39} - 30 q^{42} + 36 q^{46} + 26 q^{49} + 38 q^{51} - 86 q^{57} - 116 q^{58} + 88 q^{60} + 44 q^{63} - 32 q^{64} + 110 q^{70} + 86 q^{72} - 52 q^{78} - 156 q^{79} + 68 q^{81} - 30 q^{84} + 8 q^{85} - 112 q^{88} + 42 q^{91} + 56 q^{93} + 70 q^{99}+O(q^{100}) \) 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9 - 60 * q^16 + 2 * q^18 - 80 * q^22 - 36 * q^25 + 8 * q^28 + 24 * q^30 - 34 * q^36 + 4 * q^37 - 66 * q^39 - 30 * q^42 + 36 * q^46 + 26 * q^49 + 38 * q^51 - 86 * q^57 - 116 * q^58 + 88 * q^60 + 44 * q^63 - 32 * q^64 + 110 * q^70 + 86 * q^72 - 52 * q^78 - 156 * q^79 + 68 * q^81 - 30 * q^84 + 8 * q^85 - 112 * q^88 + 42 * q^91 + 56 * q^93 + 70 * q^99

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